Europeean Materials Modelling Ontology
Version 1.0.0-alpha
European Materials Modelling Counsil (EMMC)
March 22, 2020
Abstract:
EMMO is an ontology that is created by the Europeean Materials Modelling Council (EMMC) to provide a formal way to describe the fundamental concepts of physics, chemistry and materials science. EMMO is designed to pave the road for semantic interoperability providing a generic common ground for describing materials, models and data that can be adapted by all domains.
It is a representational framework of predefined classes and axioms (ontology) provided by experts (EMMC) that enables end users (industry, research, academy) to represent real life physical entities (materials, devices), models and properties using ontological signs (individuals) in a standard way to facilitate interactions and exchanges (data, software, knowledge) between all involved material modelling and characterization communities and stakeholders.Content
EMMO is a multidisciplinary effort to develop a standard representational framework (the ontology) based on current materials modelling knowledge, including physical sciences, analytical philosophy and information and communication technologies. This multidisciplinarity is illustrated by the figure on the title page. It provides the connection between the physical world, materials characterisation world and materials modelling world.
EMMO is based on and is consistent with the Review of Materials Modelling, CEN Workshop Agreement and MODA template. However, while these efforts are written for humans, EMMO is defined using the Web Ontology Language (OWL), which is machine readable and allows for machine reasoning. In terms of semantic representation, EMMO brings everything to a much higher level than these foundations.
As illustrated in the figure below, EMMO covers all aspects of materials modelling and characterisation, including:
EMMO is released under the Creative Commons license and is available at emmo.info/. The OWL2-DL sources are available in RDF/XML format.
In short, an ontology is a specification of a conceptualization. The word ontology has a long history in philosophy, in which it refers to the subject of existence. The so-called ontological argument for the existence of God was proposed by Anselm of Canterbury in 1078. He defined God as “that than which nothing greater can be thought”, and argued that “if the greatest possible being exists in the mind, it must also exist in reality. If it only exists in the mind, then an even greater being must be possible – one which exists both in the mind and in reality”. Even though this example has little to do with todays use of ontologies in e.g. computer science, it illustrates the basic idea; the ontology defines some basic premises (concepts and relations between them) from which it is possible reason to gain new knowledge.
For a more elaborated and modern definition of the ontology we refer the reader to the one provided by Tom Gruber (2009). Another useful introduction to ontologies is the paper Ontology Development 101: A Guide to Creating Your First Ontology by Noy and McGuinness (2001), which is based on the Protege sortware, with which EMMO has been developed.
A taxonomy is a hierarchical representation of classes and subclasses connected via is_a relations. Hence, it is a subset of the ontology excluding all but the is_a relations. The main use of taxonomies is for the organisation of classifications. The figure shows a simple example of a taxonomy illustrating a categorisation of four classes into a hierarchy of more higher of levels of generality.
In EMMO, the taxonomy is a rooted directed acyclic graph (DAG). This is important since many classification methods relies on this property, see e.g. Valentini (2014) and Robison et al (2015). Note, that EMMO is a DAG does not prevent some classes from having more than one parent. A Variable is for instance both a Mathematical and a Symbol. See appendix for the full EMMO taxonomy.
Individuals are the basic, “ground level” components of EMMO. They may include concrete objects such as cars, flowers, stars, persons and molecules, as well as abstract individuals such as a measured height, a specific equation and software programs.
Individuals possess attributes in form of axioms that are defined by the user (interpreter) upon declaration.
Classes represent concepts. They are the building blocks that we use to create an ontology as a representation of knowledge. We distinguish between defined and non-defined classes.
Defined classes are defined by the requirements for being a member of the class. In the graphical representations of EMMO, defined classes are orange. For instance, in the graph of the top-level entity branch below, The root EMMO and a defined class (defined to be the disjoint union of Item and Collection).
Non-defined classes are defined as an abstract group of objects, whose members are defined as belonging to the class. They are yellow in the graphical representations.
Axioms are propositions in a logical framework that define the relations between the individuals and classes. They are used to categorise individuals in classes and to define the defined classes.
The simplest form of a class axiom is a class description that just states the existence of the class and gives it an unique identifier. In order to provide more knowledge about the class, class axioms typically contain additional components that state necessary and/or sufficient characteristics of the class. OWL contains three language constructs for combining class descriptions into class axioms:
Subclass (rdfs:subClassOf) allows one to say that the class extension of a class description is a subset of the class extension of another class description.
Equivalence (owl:equivalentClass) allows one to say that a class description has exactly the same class extension (i.e. the individuals associated with the class) as another class description.
Distjointness (owl:disjointWith) allows one to say that the class extension of a class description has no members in common with the class extension of another class description.
See the section about Description logic for more information about these language constructs. Axioms are also used to define relations between relations. These are further detailed in the chapter on Relations.
EMMO build upon several theoretical frameworks.
Semiotics is the study of meaning-making. It is the dicipline of formulating something that possibly can exist in a defined space and time in the real world.
Mereotopology is the combination of mereology (science of parthood) and topology (mathematical study of the geometrical properties and conservation through deformations). It is introdused via the Item class and based on the mereotopological relations. Items in EMMO are always topologically connected in space and time. EMMO makes a strong distinction between membership and parthood relations. In contrast to collections, items can only have parts that are themselves items. For further information, see Casati and Varzi “Parts and Places” (1999).
EMMO is strongly based on physics, with the aim of being able to describe all aspects and all domains of physics, from quantum mechanics to continuum, engeneering, chemistry, etc. EMMO is compatible with both the De Broglie - Bohm and the Copenhagen interpretation of quantum mecanics (see Physical for more comments).
EMMO defines a physics-based parthood hierachy under Physical by introducing the following concepts (illustrated in the figure below):
Elementary is the fundamental, non-divisible constituent of entities. In EMMO, elementaries are based on the standard model of physics.
State is a Physical whose parts does not change during its life time (at the chosen level of granularity). This is consistent with a state within e.g. thermodynamics.
Existent is a succession of states.
Physical.Metrology is the science of measurements. It introduces units and links them to properties. The description of metrology in EMMO is based on the standards of International System of Quantities (ISQ) and International System of Units (SI).
Description logic (DL) is a formal knowledge representation language in which the axioms are expressed. It is less expressive than first-order logic (FOL), but commonly used for providing the logical formalism for ontologies and semantic web. EMMO is expressed in the Web Ontology Language (OWL), which in turn is based on DL. This brings along features like reasoning.
Since it is essential to have a basic notion of OWL and DL, we include here a very brief overview. For a proper introduction to OWL and DL, we refer the reader to sources like Grau et.al. (2008), OWL2 Primer and OWL Reference.
OWL distinguishes between six types of class descriptions:
owl:oneOf)owl:someValuesFrom, owl:allValuesFrom, owl:hasValue, owl:cardinality, owl:minCardinality, owl:maxCardinality)owl:intersectionOf)owl:unionOf)owl:complementOf)Except for the first, all of these refer to defined classes. The table below shows the notation in OWL, DL and the Manchester OWL syntax, all commonly used for the definitions. The Manchester syntax is used by Protege and is designed to not use DL symbols and to be easy and quick to read and write. Several other syntaxes exist for DL. An interesting example is the pure Python syntax proposed by Lamy (2017), which is used in the open source Owlready2 Python package. The Python API for EMMO is also based on Owlready2.
| DL | Manchester | Python + Owlready2 | Read | Meaning |
|---|---|---|---|---|
| Constants | ||||
| ⊤ | Thing | top | A special class with every individual as an instance | |
| ⊥ | Nothing | bottom | The empty class | |
| Axioms | ||||
| A ≐ B | A is defined to be equal to B | Class definition | ||
| A ⊑ B | A subclass_of B | class A(B): … | all A are B | Class inclusion |
| issubclass(A, B) | Test for inclusion | |||
| A ≡ B | A equivalent_to B | A.equivalent_to.append(B) | A is equivalent to B | Class equivalence |
| B in A.equivalent_to | Test for equivalence | |||
| a : A | a is_a A | a = A() | a is a A | Class assertion (instantiation) |
| isinstance(a, A) | Test for instance of | |||
| (a, b) : R | a object property assertion b | a.R.append(b) | a is R-related to b | Property assertion |
| (a, n) : R | a data property assertion n | a.R.append(n) | a is R-related to n | Data assertion |
| Constructions | ||||
| A ⊓ B | A and B | A & B | A and B | Class intersection (conjunction) |
| A ⊔ B | A or B | A | B | A or B | Class union (disjunction) |
| ¬A | not A | Not(A) | not A | Class complement (negation) |
| {a, b, ...} | {a, b, …} | OneOf([a, b, …]) | one of a, b, … | Class enumeration |
| S ≡ R− | S inverse_of R | Inverse(R) | S is inverse of R | Property inverse |
| S.inverse == R | Test for inverse | |||
| ∀R.A | R only A | R.only(A) | all A with R | Universal restriction |
| ∃R.A | R some A | R.some(A) | some A with R | Existential restriction |
| = nR.A | R exactly n A | R.exactly(n, A) | Cardinality restriction | |
| ≤ nR.A | R min n A | R.min(n, A) | Minimum cardinality restriction | |
| ≥ nR.A | R max n A | R.max(n, A) | Minimum cardinality restriction | |
| ∃R{a} | R value a | R.value(a) | Value restriction | |
| Decompositions | ||||
| A ⊔ B ⊑ ⊥ | A disjoint with B | AllDisjoint([A, B]) | A disjoint with B | Disjoint |
| B in A.disjoints() | Test for disjointness | |||
| ∃R.⊤ ⊑ A | R domain A | R.domain = A | Classes that the restriction applies to | |
| ⊤ ⊑ ∀R.B | R range B | R.range = B | All classes that can be the value of the restriction |
Here are some examples of different class descriptions using both the DL and Manchester notation.
owl:equivalentTo)Equivalence (≡) defines necessary and sufficient conditions.
Parent is equivalent to mother or father
DL: parent ≡ mother ∨ father
Manchester: parent equivalent_to mother or father
rdf:subclassOf)Inclusion (⊑) defines necessary conditions.
An employee is a person.
DL: employee ⊑ person
Manchester: employee is_a person
owl:oneOf)The color of a wine is either white, rose or red:
DL: wine_color ≡ {white, rose, red}
Manchester: wine_color equivalent_to {white, rose, red}
owl:someValuesFrom)A mother is a woman that has a child (some person):
DL: mother ≡ woman ⊓ ∃has_child.person
Manchester: mother equivalent_to woman and has_child some person
owl:allValuesFrom)All parents that only have daughters:
DL: parents_with_only_daughters ≡ person ⊓ ∀has_child.woman
Manchester: parents_with_only_daughters equivalent_to person and has_child only woman
owl:hasValue)The owl:hasValue restriction allows to define classes based on the existence of particular property values. There must be at least one matching property value.
All children of Mary:
DL: Marys_children ≡ person ⊓ ∃has_parent.{Mary}
Manchester: Marys_children equivalent_to person and has_parent value Mary
owl:cardinality)The owl:cardinality restrictions (≥, ≤ or ≡) allow to define classes based on the maximum (owl:maxCardinality), minimum (owl:minCardinality) or exact (owl:cardinality) number of occurences.
A person with one parent:
DL: half_orphant ≡ person and =1has_parent.person
Manchester: half_orphant equivalent_to person and has_parent exactly 1 person
owl:intersectionOf)Individuals of the intersection (⊓) of two classes, are simultaneously instances of both classes.
A man is a person that is male:
DL: man ≡ person ⊓ male
Manchester: man equivalent_to person and male
owl:unionOf)Individuals of the union (⊔) of two classes, are either instances of one or both classes.
A person is a man or woman:
DL: person ≡ man ⊔ woman
Manchester: person equivalent_to man or woman
owl:complementOf)Individuals of the complement (¬) of a class, are all individuals that are not member of the class.
Not a man:
DL: female ≡ ¬ male
Manchester: female equivalent_to not male
The EMMO ontology is structured in shells, expressed by specific ontology fragments, that extends from fundamental concepts to the application domains, following the dependency flow.
The EMMO top level is the group of fundamental axioms that constitute the philosophical foundation of the EMMO. Adopting a physicalistic/nominalistic perspective, the EMMO defines real world objects as 4D objects that are always extended in space and time (i.e. real world objects cannot be spaceless nor timeless). For this reason abstract objects, i.e. objects that does not extend in space and time, are forbidden in the EMMO.
EMMO is strongly based on the analytical philosophy dicipline semiotic. The role of abstract objects are in EMMO fulfilled by semiotic objects, i.e. real world objects (e.g. symbol or sign) that stand for other real world objects that are to be interpreted by an agent. These symbols appear in actions (semiotic processes) meant to communicate meaning by establishing relationships between symbols (signs).
Another important building block of from analytical philosophy is atomistic mereology applied to 4D objects. The EMMO calls it ‘quantum mereology’, since the there is a epistemological limit to how fine we can resolve space and time due to the uncertanity principles.
The mereotopology module introduces the fundamental mereotopological concepts and their relations with the real world objects that they represent. The EMMO uses mereotopology as the ground for all the subsequent ontology modules. The concept of topological connection is used to define the first distinction between ontology entities namely the Item and Collection classes. Items are causally self-connected objects, while collections are causally disconnected. Quantum mereology is represented by the Quantum class. This module introduces also the fundamental mereotopological relations used to distinguish between space and time dimensions.
The physical module, defines the Physical objects and the concept of Void that plays a fundamental role in the description of multiscale objects and quantum systems. It also define the Elementary class, that restricts mereological atomism in space.
In EMMO, the only univocally defined real world object is the Item individual called Universe that stands for the universe. Every other real world object is a composition of elementaries up to the most comprehensive object; the Universe. Intermediate objects are not univocally defined, but their definition is provided according to some specific philosophical perspectives. This is an expression of reductionism (i.e. objects are made of sub-objects) and epistemological pluralism (i.e. objects are always defined according to the perspective of an interpreter, or a class of interpreters).
The Perspective class collects the different ways to represent the objects that populate the conceptual region between the elementary and universe levels.
The middle level ontologies act as roots for extending the EMMO towards specific application domains.
The Reductionistic perspective class uses the fundamental non-transitive parthood relation, called direct parthood, to provide a powerful granularity description of multiscale real world objects. The EMMO can in principle represents the Universe with direct parthood relations as a direct rooted tree up to its elementary constituents.
The Phenomenic perspective class introduces the concept of real world objects that express of a recognisable pattern in space or time that impress the user. Under this class the EMMO categorises e.g. formal languages, pictures, geometry, mathematics and sounds. Phenomenic objects can be used in a semiotic process as signs.
The Physicalistic perspective class introduces the concept of real world objects that have a meaning for the under applied physics perspective.
The Holistic perspective class introduces the concept of real world objects that unfold in time in a way that has a meaning for the EMMO user, through the definition of the classes Process and Participant. The semiotics module introduces the concepts of semiotics and the Semiosis process that has a Sign, an Object and an Interpreter as participants. This forms the basis in EMMO to represent e.g. models, formal languages, theories, information and properties.
All EMMO relations are subrelations of the relations found in the two roots: mereotopological and semiotical. The relation hierarchy extends more vertically (i.e. more subrelations) than horizontally (i.e. less sibling relations), facilitating the categorisation and inferencing of individuals. See also the chapter EMMO Relations.
Imposing all relations to fall under mereotopology or semiotics is how the EMMO force the developers to respect its perspectives. Two entities are related only by contact or parthood (mereotopology) or by standing one for another (semiosis): no other types of relation are possible within the EMMO.
A unique feature in EMMO, is the introduction of direct parthood. As illustrated in the figure below, it is a mereological relation that lacks transitivity. This makes it possible to entities made of parts at different levels of granularity and to go between granularity levels in a well-defined manner. This is paramount for cross scale interoperability. Every material in EMMO is placed on a granularity level and the ontology gives information about the direct upper and direct lower level classes using the non-transitive direct parthood relations.
All entities and relations in EMMO have some attributes, called annotations. In some cases, only the required International Resource Identifier (IRI) and relations are provided. However, descriptive annotations, like elucidation and comment, are planned to be added for all classes and relations. Possible annotations are:
In the language of OWL, relations are called properties. However, since relations describe relations between classes and individuals and since properties has an other meaning in EMMO, we only call them relations.
Resource Description Framework (RDF) is a W3C standard that is widely used for describing informations on the web and is one of the standards that OWL builds on. RDF expresses information in form of subject-predicate-object triplets. The subject and object are resources (aka items to describe) and the predicate expresses a relationship between the subject and the object.
In OWL are the subject and object classes or individuals (or data) while the predicate is a relation. An example of an relationship is the statement dog is_a animal. Here dog is the subject, is_a the predicate and animal the object.
OWL distingues between object properties, that link classes or individuals to classes or individuals, and data properties that link individuals to data values. Since EMMO only deals with classes, we will only be discussing object properties. However, in actual simulation or characterisation applications build on EMMO, datatype propertyes will be important.
The characteristics of the different properties are described by the following property axioms:
rdf:subPropertyOf is used to define that a property is a subproperty of some other property. For instance, in the figure below showing the relation branch, we see that active_relation is a subproperty or relation. The rdf:subPropertyOf axioms forms a taxonomy-like tree for relations.
owl:equivalentProperty states that two properties have the same property extension.
owl:inverseOf axioms relate active relations to their corresponding passive relations, and vice versa. The root relation relation is its own inverse.
owl:FunctionalProperty is a property that can have only one (unique) value y for each instance x, i.e. there cannot be two distinct values y1 and y2 such that the pairs (x,y1) and (x,y2) are both instances of this property. Both object properties and datatype properties can be declared as “functional”.
owl:InverseFunctionalProperty
owl:TransitiveProperty states that if a pair (x,y) is an instance of P, and the pair (y,z) is instance of P, then we can infer that the pair (x,z) is also an instance of P.
owl:SymmetricProperty states that if the pair (x,y) is an instance of P, then the pair (y,x) is also an instance of P. A popular example of a symmetric property is the siblingOf relation.
rdfs:domain specifies which classes the property applies to. Or said differently, the valid values of the subject in a subject-predicate-object triplet.
rdfs:range specifies the property extension, i.e. the valid values of the object in a subject-predicate-object triplet.
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_ec2472ae_cf4a_46a5_8555_1556f5a6c3c5
Elucidation: The superclass of all relations used by the EMMO.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_517dfaf9_4970_41ac_81ee_d031627d2c7c
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_03212fd7_abfd_4828_9c8e_62c293052d4b
Elucidation: The superclass of all EMMO mereotopological relations.
Comment: Mereotopology merges mereological and topological concepts and provides relations between wholes, parts, boundaries, etc.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_9cb984ca_48ad_4864_b09e_50d3fff19420
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_4d6504f1_c470_4ce9_b941_bbbebc9ab05d
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_8c898653_1118_4682_9bbf_6cc334d16a99
Comment: Enclosure is reflexive and transitive.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_6703954e_34c4_4a15_a9e7_f313760ae1a8
Comment: Causality is a topological property between connected items.
Comment: Items being connected means that there is a topological contact or “interaction” between them.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_d893d373_b579_4867_841e_1c2b31a8d2c6
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_8ef3cd6d_ae58_4a8d_9fc0_ad8f49015cd0
Comment: Relates a quantity to its reference unit through spatial direct parthood.
Relations:
IRI: http://emmo.info/emmo/middle/reductionistic#EMMO_663859e5_add3_4c9e_96fb_c99399de278d
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_6b7276a4_4b9d_440a_b577_0277539c0fc4
Relations:
IRI: http://emmo.info/emmo/top/physical#EMMO_7afbed84_7593_4a23_bd88_9d9c6b04e8f6
Elucidation: A relation that isolate a proper part that covers the total spatial extension of a whole within a time interval.
Relations:
IRI: http://emmo.info/emmo/middle/reductionistic#EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe
Relations:
IRI: http://emmo.info/emmo/middle/holistic#EMMO_ae2d1a96_bfa1_409a_a7d2_03d69e8a125a
Elucidation: The relation between a process and an object participating to it.
Comment: Participation is a parthood relation: you must be part (and then be connected) of the process to contribute to it.
Comment: Participation is not under direct parthood since a process is not strictly related to reductionism, but it’s a way to categorize temporal regions by the interpreters.
Relations:
IRI: http://emmo.info/emmo/middle/holistic#EMMO_c5aae418_1622_4d02_93c5_21159e28e6c1
Relations:
IRI: http://emmo.info/emmo/middle/reductionistic#EMMO_65a2c5b8_e4d8_4a51_b2f8_e55effc0547d
Relations:
IRI: http://emmo.info/emmo/top/physical#EMMO_6e046dd0_9634_4013_b2b1_9cc468087c83
Elucidation: A relation that isolates a proper part that extends itself in time through a portion of the lifetime whole.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_9380ab64_0363_4804_b13f_3a8a94119a76
Relations:
IRI: http://emmo.info/emmo/top/physical#EMMO_f68030be_94b8_4c61_a161_886468558054
Elucidation: A relation that isolates a proper part that extends itself in time within the overall lifetime of the whole, without covering the full spatial extension of the 4D whole (i.e. is not a temporal part).
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_17e27c22_37e1_468c_9dd7_95e137f73e7f
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_67fc0a36_8dcb_4ffa_9a43_31074efa3296
Comment: Relates the physical quantity to its unit through spatial direct parthood.
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_2337e25c_3c60_43fc_a8f9_b11a3f974291
Elucidation: The generic EMMO semiotical relation.
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_60577dea_9019_4537_ac41_80b0fb563d41
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_24c71baf_6db6_48b9_86c8_8c70cf36db0c
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_39c3815d_8cae_4c8f_b2ff_eeba24bec455
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_eb3518bf_f799_4f9e_8c3e_ce59af11453b
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_297999d6_c9e4_4262_9536_bd524d1c6e21
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_7fb7fe7e_bdf9_4eeb_adad_e384dd5285c6
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_e1097637_70d2_4895_973f_2396f04fa204
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_bed1d005_b04e_4a90_94cf_02bc678a8569
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_3446e167_c576_49d6_846c_215bb8878a55
Relations:
emmo is a class representing the collection of all the individuals (signs) that are used in the ontology. Individuals are declared by the EMMO users when they want to apply the EMMO to represent the world.
The root of all classes used to represent the world. It has two children; collection and item.
collection is the class representing the collection of all the individuals (signs) that represents a collection of non-connected real world objects.
item Is the class that collects all the individuals that are members of a set (it’s the most comprehensive set individual). It is the branch of mereotopology.
IRI: http://emmo.info/emmo/top/physical#EMMO_c5ddfdba_c074_4aa4_ad6b_1ac4942d300d
Elucidation: A ‘Item’ that has part some ‘Elementary’ and whose temporal proper parts are only ‘Physical’-s (i.e. it can be perceived without interruptions in time).
Comment: A ‘Physical’ is the class that contains all the individuals that stand for real world objects that interact physically with the ontologist, i.e. physical objects.
A physical object must be perceived through physical interaction by the ontologist. Then the ontologist can declare an individual standing for the physical object just perceived.
Perception is a subcategory of physical interactions. It is an interaction that stimulate a representation of the physical object within the ontologist (the agent).
Comment: A ‘Physical’ must include at least an ‘Elementary’ part, and can include ‘Void’ parts.
A ‘Physical’ may include as part also the ‘Void’ surrounding or enclosed by its ‘Physical’ sub parts.
There are no particular criteria for ‘Physical’-s structure, except that is made of some ‘Elementary’-s as proper parts and not only ‘Void’.
This is done in order to take into account the quantum nature of physical systems, in which the actual position of sub-components (e.g. electrons in an atom) is not known except for its probability distribution function (according to the Copenhagen interpretation.)
e.g. a real world object that has spatial parts an atom and a cubic light year of void, extending for some time, can be a physical object.
Comment: A ‘Physical’ with dimensions other than 4D cannot exist, following the restriction of the parent ‘EMMO’ class.
It follows from the fact that perception is always unfolding in time.
e.g. you always have an aperture time when you take a picture or measure a property. Instantaneous perceptions are idealizations (abstractions) or a very small time measurement.
Comment: From Latin physica “study of nature” (and Ancient Greek φυσικός, “natural”).
Here the word relates to things perceived through the senses as opposed to the mind; tangible or concrete.
Comment: In the EMMO there are no relations such as occupiesSpace, since ‘Physical’-s are themselves the 4D regions.
Comment: The EMMO can be used to represent real world entities as ‘Physical’-s that are easy to connect to classical or quantum mechanical based models.
Classical mechanics poses no representational issues, for the EMMO: the 4D representation of ‘Physical’-s is consistent with classical physics systems.
However, the representation of ‘Physical’-s that are typically analized through quantum mechanics (e.g. molecules, atoms, clusters), is not straightforward.
While this approach is really easy to implement in an ontology, since each entity has its own well defined 4D region, its mathematical representation failed to receive large consensus due to the difficulties to include relativistic effects, to be extended to subnuclear scale and the strong non-locality assumtpion of the quantum field.
Nevertheless, the Bohmian mechanics is a numerical approach that is used in electronic models to reduce the computational effort of the solution of Schroedinger Equation.
In practice, an EMMO user can declare a ‘physical’ individual that stand for the whole quantum system to be described, and at the same time all sub-parts individuals can be declared, having them a well defined position in time, according to De Broglie - Bohm interpretation. The Hamiltonian can be calculated by considering the sub-part individuals.
‘physical’-s are then made of ‘physical’ parts and ‘void’ parts that stand for the space between ‘physical’-s (e.g. the void between electrons and nucleus in an atom).
Upon measurement, the wavefunction collapses to a combination of close eigenstates that provide information about bservables of the system components (e.g. position, energy).
The EMMO can be used to represent ‘physical’-s that can be related to Copenhagen based models. In practice, the user should follow these steps:
define the quantum system as a ‘physical’ individual (e.g. an H2 molecule) under a specific class (e.g. ‘h2_molecule’). This individual is the whole.
define the axioms of the class that describe how many sub-parts are expected for the whole and their class types (e.g. ‘h2_molecule’ has axioms ‘has_proper_part exactly 2 electron’ and ’has_proper_part exactly 2 nucleus)
the user can now connect the whole to a Schroedinger equation based model whose Hamiltonian is calculated trough the information coming only from the axioms. No individuals are declared for the subparts!
a measurement done on the quantum system that provides information on the sub-part observables is interpreted as wavefunction collapse and leads to the end of the whole and the declaration of the sub-parts individuals which can be themselves other quantum systems
e.g. if the outer electron of the H2 molecule interacts with another entity defining its state, then the whole that stands for the entangled H2 molecule becomes a ‘physical’ made of an electron individual, a quantum system made of one electron and two nuclei and the void between them.
e.g. in the Born-Oppenheimer approximation the user represent the atom by un-entangling nucleus and electronic cloud. The un-entanglement comes in the form of declaration of individual as parts.
e.g. the double slit experiment can be represent in the EMMO as: a) before the slit: a ‘physical’ that extend in space and has parts ‘electron’ and ‘void’, called ‘single_electron_wave_function’. ‘electron’ and ‘void’ are only in the axioms and not decalred individuals. b) during slit passage: a ‘physical’ made of one declared individual, the ‘electron’. c) after the slit: again ‘single_electron_wave_function’ d) upon collision with the detector: ‘physical’ made of one declared individual, the ‘electron’.
Comment: The purpose of the ‘Physical’ branch is to provide a representation of the real world objects, while the models used to name, explain or predict the behaviour of the real world objects lay under the ‘Semiotic’ branch.
More than one semiotic representation can be connected to the same ‘Physical’.
e.g. Navier-Stokes or Euler equation applied to the same fluid are an example of mathematical model used to represent a physical object for some specific interpreter.
Relations:
Individuals:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_eb3a768e_d53e_4be9_a23b_0714833c36de
Comment: A real world object is self-connected if any two parts that make up the whole are connected to each other (here the concept of connection is primitive).
Alternatively, using the primitive path-connectivity concept we can define a self-connected real world object as an object for which each couple of points is path-connected.
Comment: An ‘Item’ individual stands for a real world self-connected object which can be represented as a whole made of connected parts (e.g. a car made of components).
In the EMMO, connectivity is the topological foundation of causality.
All physical systems, i.e. systems whose behaviour is explained by physics laws, are represented only by ‘Item’-s.
Members of a ‘Collection’ lack of causality connection, i.e. they do not constitute a physical system as a whole.
Comment: From Latin item, “likewise, just so, moreover”.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_802d3e92_8770_4f98_a289_ccaaab7fdddf
Elucidation: The class representing the collection of all the individuals declared in this ontology standing for real world objects.
Comment: ‘EMMO’ is the disjoint union of ‘Item’ and ‘Collection’ (covering axiom).
The union implies that ‘EMMO’ individuals can only be ‘Item’ individuals (standing for self-connected real world objects) or ‘Collection’ individuals (standing for a collection of disconnected items).
Disjointness means that a ‘Collection’ individual cannot be an ‘Item’ individual and viceversa, representing the fact that a real world object cannot be self-connected and non-self connected at the same time.
Comment: For the EMMO ontologist the whole universe is represented as a 4D path-connected topological manifold (i.e. the spacetime).
A real world object is then a 4D topological sub-region of the universe.
A universe sub-region is isolated and defined as a real world object by the ontologist. Then, through a semiotic process that occurs at meta-ontological level (i.e. outside the ontology). an EMMO ontology entity (e.g. an OWL individual) is assigned to represent that real world object.
The fundamental distinction between real world objects, upon which the EMMO is based, is self-connectedness: a real world object can be self-connected xor not self-connected.
Comment: In the EMMO we will refer to the universe as a Minkowski space, restricting the ontology to special relativity only. However, exension to general relativity, will adding more complexity, should not change the overall approach.
Comment: Mereotopology is the fundamental logical representation used by the EMMO ontologist to characterize the universe and to provide the definitions to connect real world objects to the EMMO concepts.
Parthood relations do not change dimensionality of the real world object referred by an ‘EMMO’ individual, i.e. every part of a real world object always retains its 4D dimensionality.
The smallest part of a real world object (i.e. a part that has no proper parts) is referred in the EMMO by a ‘Quantum’ individual.
It follows that, for the EMMO, real world objects of dimensionality lower than 4D (e.g. surfaces, lines) do not exist.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_3f9ae00e_810c_4518_aec2_7200e424cf68
Elucidation: The class of ‘EMMO’ individuals that stand for real world objects that can’t be further divided in time nor in space.
Example: For a physics based ontology the ‘Quantum’ can stand for the smallest identifiable portion of spacetime defined by the Planck limit in length (1.616e-35 m) and time (5.39e-44 s).
However, the quantum mereotopology approach is not restricted only to physics. For example, in a manpower management ontology, a ‘Quantum’ can stand for an hour (time) of a worker (space) activity.
Comment: A ‘Quantum’ is the most fundamental subclass of ‘Item’, since its individuals stand for the smallest possible self-connected 4D real world objects.
The quantum concept recalls the fact that there is lower epistemological limit to our knowledge of the universe, related to the uncertainity principle.
Comment: A ‘Quantum’ stands for a 4D real world object.
Comment: A quantum is the EMMO mereological 4D a-tomic entity.
To avoid confusion with the concept of atom coming from physics, we will use the expression quantum mereology, instead of a-tomistic mereology.
Comment: From Latin quantum (plural quanta) “as much as, so much as;”, introduced in physics directly from Latin by Max Planck, 1900.
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_2d2ecd97_067f_4d0e_950c_d746b7700a31
Elucidation: The class of all individuals that stand for a real world not self-connected object.
Comment: A ‘Collection’ individual stands for a non-self-connected real world object.
A ‘Collection’ individual is related to each ‘Item’ individuals of the collection (i.e. the members) through the membership relation.
An ‘Item’ individual stands for a real world self-connected object which can be represented as a whole made of connected parts (e.g. a car made of components).
Comment: Formally, ‘Collection’ is axiomatized as the class of individuals that hasMember some ‘Item’.
A ‘Collection’ cannot have as member another ‘Collection’.
Comment: From Latin collectio, from colligere ‘gather together’.
Comment: e.g. the collection of users of a particular software, the collection of atoms that have been part of that just dissociated molecule, or even the collection of atoms that are part of a molecule considered as single individual non-connected objects and not as a mereotopological self-connected fusion.
Relations:
IRI: http://emmo.info/emmo/top/physical#EMMO_29072ec4_ffcb_42fb_bdc7_26f05a2e9873
Elucidation: A ‘Item’ that has no ‘Physical’ parts.
Comment: From Latin vacuus, “empty”.
Relations:
IRI: http://emmo.info/emmo/top/physical#EMMO_0f795e3e_c602_4577_9a43_d5a231aa1360
Elucidation: The basic constituent of ‘item’-s that can be proper partitioned only in time up to quantum level.
Comment: According to mereology, this should be call ‘a-tomistic’ in the strict etimological sense of the word (from greek, a-tomos: un-divisible).
Mereology based on such items is called atomistic mereology.
However, in order not to confuse the lexicon between mereology and physics (in which an atom is a divisible physical entity) we prefer to call it ‘elementary’, recalling the concept of elementary particle coming from the standard particles model.
Comment: From Latin elementārius (“elementary”), from elementum (“one of the four elements of antiquity; fundamentals”)
Comment: While a ‘Quantum’ is a-tomistic in time and space, an ‘elementary’ is a-tomistic only in space, recalling the concept of elementary particle.
Relations:
IRI: http://emmo.info/emmo/top#EMMO_49267eba_5548_4163_8f36_518d65b583f9
Elucidation: The class of individuals that stand for real world objects according to a specific representational perspective.
Comment: This class is the practical implementation of the EMMO pluralistic approach for which that only objective categorization is provide by the Universe individual and all the ‘Elementary’ individuals.
Between these two extremes, there are several subjective ways to categorize real world objects, each one provide under a ‘Perspective’ subclass.
Relations:
IRI: http://emmo.info/emmo/middle/manufacturing#EMMO_494b372c_cfdf_47d3_a4de_5e037c540de8
Relations:
IRI: http://emmo.info/emmo/middle/manufacturing#EMMO_86ca9b93_1183_4b65_81b8_c0fcd3bba5ad
Elucidation: A ‘physical’ that stands for a real world object that has been manufacturedfor a particular purpose.
Example: Car, tire, composite material.
Comment: The ‘Engineered’ branch represents real world objects that show some level of complexity/heterogeneity in their composition, and are made for a specific use.
Relations:
IRI: http://emmo.info/emmo/middle/holistic#EMMO_49804605_c0fe_4538_abda_f70ba1dc8a5d
Elucidation: A portion of a ‘Process’ that participates to the process with a specific role.
Comment: In the EMMO the relation of participation to a process falls under mereotopology.
Since topological connection means causality, then the only way for a real world object to participate to a process is to be a part of it.
Relations:
IRI: http://emmo.info/emmo/middle/manufacturing#EMMO_e775e341_5687_4d45_b50c_379b098a8c26
Relations:
IRI: http://emmo.info/emmo/middle/holistic#EMMO_0277f24a_ea7f_4917_81b7_fb0406c8fc62
Elucidation: A union of classes that categorize physicals under a holistic perspective, meaning that the interest is on the whole 4D object (process) and the role of its spatial parts (participants) without going further into its subparts.
Comment: An holistic perspective considers each part of the whole as equally important, without the need of a granularity hierarchy, assigning a role to the whole.
Meaning that a molecule of a body can have role in the body evolution, without caring if its part of a specific organ.
This class allows the picking of parts without necessarily going trough a rigid hierarchy of compositions (e.g. body -> organ -> cell -> molecule).
Comment: Holism (from Greek ὅλος holos “all, whole, entire”)
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_b803f122_4acb_4064_9d71_c1e5fd091fc9
Elucidation: The class of individuals that stands for semiotic objects, i.e. objects that take part on a semiotic process.
Comment: Semiotic subclasse are defined using Peirce’s semiotic theory.
“Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.” (Peirce 1902, NEM 4, 20–21).
The triadic elements: - ‘sign’: the sign A (e.g. a name) - ‘interpretant’: the sign B as the effects of the sign A on the interpreter (e.g. the mental concept of what a name means) - ‘object’: the object C (e.g. the entity to which the sign A and B refer to)
This class includes also the ‘interpeter’ i.e. the entity that connects the ‘sign’ to the ‘object’
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_b21a56ed_f969_4612_a6ec_cb7766f7f31d
Elucidation: An ‘Physical’ that is used as sign (“semeion” in greek) that stands for another ‘Physical’ through an semiotic process.
Example: A novel is made of chapters, paragraphs, sentences, words and characters (in a direct parthood mereological hierarchy).
Each of them are ‘sign’-s.
A character can be the a-tomistic ‘sign’ for the class of texts.
The horizontal segment in the character “A” is direct part of “A” but it is not a ‘sign’ itself.
For plain text we can propose the ASCII symbols, for math the fundamental math symbols.
Comment: A ‘Sign’ can have temporal-direct-parts which are ‘Sign’ themselves.
A ‘Sign’ usually have ‘sign’ spatial direct parts only up to a certain elementary semiotic level, in which the part is only a ‘Physical’ and no more a ‘Sign’ (i.e. it stands for nothing). This elementary semiotic level is peculiar to each particular system of signs (e.g. text, painting).
Just like an ‘Elementary’ in the ‘Physical’ branch, each ‘Sign’ branch should have an a-tomistic mereological part.
Comment: According to Peirce, ‘Sign’ includes three subcategories: - symbols: that stand for an object through convention - indeces: that stand for an object due to causal continguity - icon: that stand for an object due to similitudes e.g. in shape or composition
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_0cd58641_824c_4851_907f_f4c3be76630c
Elucidation: A ‘Sign’ that stands for an ‘Object’ due to causal continguity.
Example: Smoke stands for a combustion process (a fire). My facial expression stands for my emotional status.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_3ee80521_3c23_4dd1_935d_9d522614a3e2
Elucidation: A unit symbol that stands for a derived unit.
Example: Pa stands for N/m2 J stands for N m
Comment: Special units are semiotic shortcuts to more complex composed symbolic objects.
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_054af807_85cd_4a13_8eba_119dfdaaf38b
Elucidation: The interpreter’s internal representation of the object in a semiosis process.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_1b52ee70_121e_4d8d_8419_3f97cd0bd89c
Elucidation: An ‘interpreter’ that perceives another ‘entity’ (the ‘object’) through a specific perception mechanism and produces a ‘property’ (the ‘sign’) that stands for the result of that particular perception.
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_0527413c_b286_4e9c_b2d0_03fb2a038dee
Elucidation: The entity (or agent, or observer, or cognitive entity) who connects ‘Sign’, ‘Interpretant’ and ‘Object’.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_f2d5d3ad_2e00_417f_8849_686f3988d929
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_32129fb5_df25_48fd_a29c_18a2f22a2dd5
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_6f5af708_f825_4feb_a0d1_a8d813d3022b
Elucidation: The object, in Peirce semiotics.
Comment: Here is assumed that the concept of ‘object’ is always relative to a ‘semiotic’ process. An ‘object’ does not exists per se, but it’s always part of an interpretation.
The EMMO relies on strong reductionism, i.e. everything real is a formless collection of elementary particles: we give a meaning to real world entities only by giving them boundaries and defining them using ‘sign’-s.
In this way the ‘sign’-ed entity become and ‘object’, and the ‘object’ is the basic entity needed in order to apply a logical formalism to the real world entities (i.e. we can speak of it through its sign, and use logics on it through its sign).
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_35d2e130_6e01_41ed_94f7_00b333d46cf9
Elucidation: A ‘Sign’ that stands for an ‘Object’ through convention, norm or habit, without any resemblance to it.
Comment: In Peirce semiotics this kind of sign category is called symbol. However, since symbol is also used in formal languages, the name is changed in conventional.
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_d1d436e7_72fc_49cd_863b_7bfb4ba5276a
Example: viscosity in the Navier-Stokes equation
Comment: A ‘variable’ whose value is assumed to be known independently from the equation, but whose value is not explicitated in the equation.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_9c32fd69_f480_4130_83b3_fb25d9face14
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_db9a009e_f097_43f5_9520_6cbc07e7610b
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895
Elucidation: A ‘Variable’ is a symbolic object that stands for a numerical defined ‘Mathematical’ object like e.g. a number, a vector, a matrix.
Example: x k
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_8d2d9374_ef3a_47e6_8595_6bc208e07519
Elucidation: A ‘conventional’ that stand for a ‘physical’.
Comment: The ‘theory’ is e.g. a proposition, a book or a paper whose sub-symbols suggest in the mind of the interpreter an interpretant structure that can represent a ‘physical’.
It is not an ‘icon’ (like a math equation), because it has no common resemblance or logical structure with the ‘physical’.
In Peirce semiotics: legisign-symbol-argument
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_ae15fb4f_8e4d_41de_a0f9_3997f89ba6a2
Elucidation: A ‘varaible’ that stand for a well known constant.
Example: π refers to the constant number ~3.14
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_f19ff3b4_6bfe_4c41_a2b2_9affd39c140b
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_fe7e56ce_118b_4243_9aad_20eb9f4f31f6
Elucidation: The dependent variable for which an equation has been written.
Example: Velocity, for the Navier-Stokes equation.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_d8aa8e1f_b650_416d_88a0_5118de945456
Elucidation: A quantitative property attributed by agreement to a quantity for a given purpose.
Example: The thermal conductivity of a copper sample in my laboratory can be assumed to be the conductivity that appears in the vendor specification. This value has been obtained by measurement of a sample which is not the one I have in my laboratory. This conductivity value is then a conventional quantitiative property assigned to my sample through a semiotic process in which no actual measurement is done by my laboratory.
If I don’t believe the vendor, then I can measure the actual thermal conductivity. I then perform a measurement process that semiotically assign another value for the conductivity, which is a measured property, since is part of a measurement process.
Then I have two different physical quantities that are properties thanks to two different semiotic processes.
Comment: A property that is associated to an object by convention, or assumption.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_d0200cf1_e4f4_45ae_873f_b9359daea3cd
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_873b0ab3_88e6_4054_b901_5531e01f14a4
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_dd4a7f3e_ef56_466c_ac1a_d2716b5f87ec
Elucidation: A ‘Quantity’ that can be quantified with respect to a standardized reference physical instance (e.g. the prototype meter bar, the kg prototype) or method (e.g. resilience) through a measurement process.
Comment: “A property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by means of a number and a reference” ISO 80000-1
“A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of such.” International vocabulary of metrology (VIM)
Comment: A quantitative property is always expresssed as a quantity (i.e. a number and a reference unit). For the EMMO, a nominalistic ontology, there is no property as abstract object.
A property is a sign that stands for an object according to a specific code shared by some observers.
For quantititative properties, one possible code that is shared between the scientific community (the observers) is the SI system of units.
Comment: Subclasses of ‘QuantitativeProperty’ classify objects according to the type semiosis that is used to connect the property to the object (e.g. by measurement, by convention, by modelling).
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_b7bcff25_ffc3_474e_9ab5_01b1664bd4ba
Elucidation: A ‘Perceptual’ referring to a specific code that is used as ‘Conventional’ sign to represent an ‘Object’ according to a specific interaction mechanism by an ‘Observer’.
(A property is always a partial representation of an ‘Object’ since it reflects the ‘Object’ capability to be part of a specific ‘Observation’ process)
Example: Hardness is a subclass of properties.
Vickers hardness is a subclass of hardness that involves the procedures and instruments defined by the standard hardness test.
Example: Let’s define the class ‘colour’ as the subclass of the properties that involve photon emission and an electromagnetic radiation sensible observer.
An individual C of this class ‘colour’ can be defined be declaring the process individual (e.g. daylight illumination) and the observer (e.g. my eyes)
Stating that an entity E has_property C, we mean that it can be observed by such setup of process + observer (i.e. observed by my eyes under daylight).
This definition can be generalized by using a generic human eye, so that the observer can be a generic human.
This can be used in material characterization, to define exactly the type of measurement done, including the instrument type.
Comment: A ‘Property’ is a sort of name or label that we put upon objects that interact with an observer in the same specific way.
e.g. “hot” objects are objects that interact with an observer through a perception mechanism aimed to perceive an heat source.
Comment: We know real world entities through observation/perception.
A non-perceivable real world entity does not exist (or it exists on a plane of existance that has no intersection with us and we can say nothing about it).
Perception/observation of a real wolrd entity occurs when the entity stimulate an observer in a peculiar way through a well defined perception channel.
For this reason each property is related to a specific observation process which involves a specific observer with its own perception mechanisms.
The observation process (e.g. a look, a photo shot, a measurement) is performed by an observer (e.g. you, a camera, an instrument) through a specific perception mechanism (e.g. retina impression, CMOS excitation, piezoelectric sensor activation) and involves an observed entity.
An observation is a semiotic process, since it stimulate an interpretant within the interpreter who can communicate the perception result to other interpreters through a sign which is the property.
Property subclasses are specializations that depend on the type of observation processes.
e.g. the property ‘colour’ is related to a process that involves emission or interaction of photon and an observer who can perceive electromagnetic radiation in the visible frequency range.
Properties usually relies on symbolic systems (e.g. for colour it can be palette or RGB).
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_2a888cdf_ec4a_4ec5_af1c_0343372fc978
Elucidation: A ‘Property’ that is determined by each ‘Observer’ following a well defined ‘Observation’ procedure through a specific perception channel.
Comment: The word objective does not mean that each observation will provide the same results. It means that the observation followed a well defined procedure.
Comment: This class refers to what is commonly known as physical property, i.e. a measurable property of physical system, whether is quantifiable or not.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_909415d1_7c43_4d5e_bbeb_7e1910159f66
Elucidation: An ‘ObjectiveProperty’ that cannot be quantified.
Example: CFC is a ‘sign’ that stands for the fact that the morphology of atoms composing the microstructure of an entity is predominantly Cubic Face Centered
A color is a nominal property.
Sex of a human being.
Comment: “Property of a phenomenon, body, or substance, where the property has no magnitude.”
“A nominal property has a value, which can be expressed in words, by alphanumerical codes, or by other means.”
International vocabulary of metrology (VIM)
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_251cfb4f_5c75_4778_91ed_6c8395212fd8
Elucidation: A ‘Property’ that cannot be univocally determined and depends on an agent (e.g. a human individual, a community) acting as black-box.
Example: The beauty of that girl. The style of your clothing.
Comment: The word subjective means that a non-well defined or an unknown procedure is used for the definition of the property.
This happens due to e.g. the complexity of the object, the lack of a underlying model for the representation of the object, the non-well specified meaning of the property symbols.
A ‘SubjectiveProperty’ cannot be used to univocally compare ‘Object’-s.
e.g. you cannot evaluate the beauty of a person on objective basis.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_939483b1_0148_43d1_8b35_851d2cd5d939
Elucidation: A ‘sign’ that not only stands for a ‘physical’ or a ‘process’, but it is also a simplified representation, aimed to assist calculations for its description or for predictions of its behaviour.
A ‘model’ represents a ‘physical’ or a ‘process’ by direct similitude (e.g. small scale replica) or by capturing in a logical framework the relations between its properties (e.g. mathematical model).
Comment: A ‘model’ prediction is always a prediction of the properties of an entity, since an entity is known by an interpreter only through perception.
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_d7788d1a_020d_4c78_85a1_13563fcec168
Elucidation: A ‘Sign’ that stands for an ‘Object’ by resembling or imitating it, in shape or by sharing a similar logical structure.
Example: A picture that reproduces the aspect of a person.
An equation that reproduces the logical connection of the properties of a physical entity.
Comment: Three subtypes of icon are possible:
the image, which depends on a simple quality (e.g. picture)
the diagram, whose internal relations, mainly dyadic or so taken, represent by analogy the relations in something (e.g. math formula, geometric flowchart)
the metaphor, which represents the representative character of a sign by representing a parallelism in something else
[Wikipedia]
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_314d0bd5_67ed_437e_a609_36d46147cea7
Elucidation: A ‘process’ that is recognized by physical sciences and is catogrized accordingly.
Comment: While every ‘process’ in the EMMO involves physical objects, this class is devoted to represent real world objects that express a phenomena relevant for the ontologist.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_22522299_4091_4d1f_82a2_3890492df6db
Elucidation: An experiment is a process that is intended to replicate a physical phenomenon in a controlled environment.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_463bcfda_867b_41d9_a967_211d4d437cfb
Elucidation: An ‘observation’ that results in a quantitative comparison of a ‘property’ of an ‘object’ with a standard reference.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_10a5fd39_06aa_4648_9e70_f962a9cb2069
Elucidation: A ‘Semiosis’ that involves an ‘Observer’ that perceives another ‘Physical’ (the ‘Object’) through a specific perception mechanism and produces a ‘Property’ (the ‘Sign’) that stands for the result of that particular perception.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_6c739b1a_a774_4416_bb31_1961486fa9ed
Elucidation: The ‘semiosis’ process of interpreting a ‘physical’ and provide a complec sign, ‘theory’ that stands for it and explain it to another interpreter.
Relations:
IRI: http://emmo.info/emmo/middle/holistic#EMMO_43e9a05d_98af_41b4_92f6_00f79a09bfce
Elucidation: A temporal part of a ‘physical’ that identifies a particular type of evolution in time.
Comment: A ‘Process’ is always a ‘Physical’, since a ‘Void’ does not have elements that evolves in time.
Comment: A ‘Process’ is defined as a temporal part of a ‘Physical’ that is categorized according to an EMMO user that recognizes a particular type of evolution in time of the real world object.
Following the common definition of process, every ‘Physical’ should be a process, since every 4D object always has a time dimension.
However, in the EMMO we restrict the meaning of the word process to ‘Physical’-s whose evolution in time have a particular meaning for the ontologist.
A ‘Process’ is not only something that unfolds in time (which is automatically represented in a 4D ontology), but something that has a meaning for the ontologist, i.e. that the ontologist can separate from the rest of the 4D physical for any reason.
Relations:
IRI: http://emmo.info/emmo/top/semiotics#EMMO_008fd3b2_4013_451f_8827_52bceab11841
Elucidation: A ‘Process’, that has participant an ‘Interpreter’, that is aimed to produce a ‘Sign’ representing another participant, the ‘Object’.
Example: Me looking a cat and saying loud: “Cat!” -> the semiosis process
me -> interpreter cat -> object (in Peirce semiotics) the cat perceived by my mind -> interpretant “Cat!” -> sign, the produced sign
Relations:
IRI: http://emmo.info/emmo/middle/manufacturing#EMMO_a4d66059_5dd3_4b90_b4cb_10960559441b
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_91756568_8655_4060_8937_a1a906dad8c1
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_0d69f94a_f4fa_49d9_bf90_ace770eeab02
Elucidation: A ‘acoustical’ that can be categorized as music by the ontologist.
Comment: A music score is not a ‘music’ individual.
A music score is a ‘graphical’ that can stand for a ‘music’ (or vice versa) since it comes through a different perception mechanism.
The ‘music’ individual is the sound itself as produced and delivered by a source in the form of sound wave through a medium.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_649bf97b_4397_4005_90d9_219755d92e34
Elucidation: A ‘Physical’ which stands for a real world object that can stimulate a perception (e.g. a mental impression, the excitation of a sensor) to an interpreter (human or non-human).
Example: A line scratched on a surface. A sound. A smell. The word ‘cat’ and the sound of the word ‘cat’ (the first one is graphical and the second acoustical).
Example: The meta-semiotic process: I see a cloud in the sky. Since I’m an EMMO ontologist, I create an individual named Cloud under the ‘Impression’ class. This semiotic process occurs at meta-level: it’s how I use the EMMO as tool for a direct representation of the world.
The semiotic process within EMMO: My friend looks at the same cloud and says: “It is an elephant”. I use the EMMO to record this experience by declaring: - my friend as MyFriend individual, belonging to ‘Interpreter’ classes - the sound of the word “elephant” as an acoustical impression individual named ElephantWord, belonging to ‘Impression’ - a relation hasSign between Cloud and ElephantWord, that makes ElephantWord also belonging to ‘Sign’ class and Cloud belonging also to ‘Object’ class - a ‘Semiosis’ individual called MyFriendElephantCloud that hasParticipant: Cloud, ElephantWord and MyFriend, respectively as object, sign and interpreter.
Comment: ‘Perceptual’ includes real world objects that: - are part of a communication system (e.g. words, speech, alphabets) - are not part of a communication system, but can be identified and referred by an interpreter
Comment: A ‘Perceptual’ is a meta-object, meaning that is addressed by the ontologist (the meta-interpreter) in a meta-semiotic process occurring outside the EMMO.
A ‘Perceptual’ becomes an ‘Object’, when it is part of a ‘Semiotic’ process described by the ontologist through the EMMO.
Comment: From Latin perceptiō (“a receiving or collecting, perception, comprehension”), from perceptus (“perceived, observed”).
Comment: This class is the most general superclass for the categorization of real world objects that are recognizable by an interpreter (agent).
A ‘Perceptual’ can stand for something else in a semiotic process (acting as sign or as object).
However, a perceptual is not necessarily a ‘Sign’ (e.g. a line sketched on a blackboard is a recognizable ‘Perceptual’ but it may stand for nothing).
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_4b3afb22_27cf_4ce3_88bc_492bfccb546b
Elucidation: An ‘impression’ which stands for a real world object whose spatiotemporal pattern makes it identifiable by an observer as a sound.
Comment: ‘acoustical’ refers to the perception mechanism of the observer that can occur through a microphone, a ear.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_660ef3b0_6692_4c51_8f69_763c7817b2e1
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_c74da218_9147_4f03_92d1_8894abca55f3
Elucidation: A ‘Phenomenic’ which stands for a real world object whose spatial configuration shows a pattern identifiable by an observer.
Example: ‘Graphical’ objects include writings, pictures, sketches …
Comment: From the Ancient Greek γραφή (graphḗ) which means drawing, painting, writing, a writing, description, and from γράφω (gráphō) which means scratch, carve.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_89a0c87c_0804_4013_937a_6fe234d9499c
Elucidation: A symbolic entity made of other symbolic entities according to a specific spatial configuration.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_1da53c06_9577_4008_8652_272fa3b62be7
Elucidation: A ‘Graphical’ that stands for a real world object that shows a recognizable pictorial pattern without being necessarily associated to a symbolic language.
Example: A drawing of a cat. A circle on a paper sheet. The Mona Lisa.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_d8d2144e_5c8d_455d_a643_5caf4d8d9df8
Elucidation: A language object is a symbolic object respecting a specific language syntactic rules (a well-formed formula).
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_50ea1ec5_f157_41b0_b46b_a9032f17ca10
Elucidation: A physical made of more than one symbol sequentially arranged.
Example: The word “cat” considered as a collection of ‘symbol’-s respecting the rules of english language.
In this example the ‘symbolic’ entity “cat” is not related to the real cat, but it is only a word (like it would be to an italian person that ignores the meaning of this english word).
If an ‘interpreter’ skilled in english language is involved in a ‘semiotic’ process with this word, that “cat” became also a ‘sign’ i.e. it became for the ‘interpreter’ a representation for a real cat.
Comment: A string is made of concatenated symbols whose arrangement is one-dimensional. Each symbol can have only one previous and one next neighborhood (bidirectional list).
Comment: A string is not requested to respect any syntactic rule: it’s simply directly made of symbols.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_057e7d57_aff0_49de_911a_8861d85cef40
Elucidation: An ‘Graphical’ that stands for a token or a composition of tokens from one or more alphabets, without necessarily respecting syntactic rules.
Example: fe780 emmo !5*a cat
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_9268958f_7f54_48ab_a693_febe2645892b
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_0ef4ff4a_5458_4f2a_b51f_4689d472a3f2
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_d7bf784a_db94_4dd9_861c_54f262846fbf
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_46f0f8df_4dc6_418f_8036_10427a3a288e
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_0c576e13_4ee7_4f3d_bfe9_1614243df018
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_b2a234a8_579a_422c_9305_b8f7e72c76cd
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_3e309118_e8b7_4021_80f4_642d2df65d94
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_0ab0485c_9e5b_4257_a679_90a2dfba5c7c
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_39362460_2a97_4367_8f93_0418c2ac9a08
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_b5957cef_a287_442d_a3ce_fd39f20ba1cd
Elucidation: A ‘graphical’ aimed to represent a geometrical concept.
Comment: A ‘geometrical’ stands for real world objects that express a geometrical concept.
This can be achieved in many different ways. For example, a line can be expressed by: a) an equation like y=mx+q, which is both an ‘equation’ and a ‘geometrical’ b) a line drawn with a pencil on a paper, which is simply a ‘graphical’ object c) a set of axioms, when the properties of a line are inferred by the interpreter reading them, that are both ‘graphical’ and also ‘formula’
The case a) is a geometrical and mathematical, b) is geometrical and pictorial, while c) is geometrical and a composition of idiomatic strings.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_86060335_31c2_4820_b433_27c64aea0366
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_25f5ca8e_8f7f_44d8_a392_bd3fe8894458
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_5f278af9_8593_4e27_a717_ccc9e07a0ddf
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_50a3552e_859a_4ff7_946d_76d537cabce6
Elucidation: A symbol that stands for a concept in the language of the meterological domain of ISO 80000.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_216f448e_cdbc_4aeb_a529_7a5fe7fc38bb
Elucidation: A symbol that stands for a single unit.
Example: Some examples are “Pa”, “m” and “J”.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_5ebd5e01_0ed3_49a2_a30d_cd05cbe72978
Elucidation: Represents the number 1, used as an explicit unit to say something has no units.
Example: Refractive index or volume fraction.
Example: Typically used for ratios of two units whos dimensions cancels out.
Qudtmatch: http://qudt.org/vocab/unit/UNITLESS
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527
Elucidation: The class of individuals that stand for an elementary mark of a specific symbolic code (alphabet).
Example: The class of letter “A” is the symbol as idea and the letter A that you see on the screen is the mark.
Comment: Subclasses of ‘Symbol’ are alphabets, in formal languages terminology.
A ‘Symbol’ is atomic for that alphabet, i.e. it has no parts that are symbols for the same alphabet. e.g. a math symbol is not made of other math symbols
A Symbol may be a String in another language. e.g. “Bq” is the symbol for Becquerel units when dealing with metrology, or a string of “B” and “q” symbols when dealing with characters.
Comment: Symbols of a formal language need not be symbols of anything. For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation in the language (e.g. parentheses).
Symbols of a formal language must be capable of being specified without any reference to any interpretation of them. (Wikipedia)
Comment: The class is the idea of the symbol, while the individual of that class stands for a specific mark (or token) of that idea.
Relations:
Individuals:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_3ee80521_3c23_4dd1_935d_9d522614a3e2
Elucidation: A unit symbol that stands for a derived unit.
Example: Pa stands for N/m2 J stands for N m
Comment: Special units are semiotic shortcuts to more complex composed symbolic objects.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_32129fb5_df25_48fd_a29c_18a2f22a2dd5
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_db716151_6b73_45ff_910c_d182fdcbb4f5
Elucidation: A set of units that correspond to the base quantities in a system of units.
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_28fbea28_2204_4613_87ff_6d877b855fcd
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_d1d436e7_72fc_49cd_863b_7bfb4ba5276a
Example: viscosity in the Navier-Stokes equation
Comment: A ‘variable’ whose value is assumed to be known independently from the equation, but whose value is not explicitated in the equation.
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_1cba0b27_15d0_4326_933f_379d0b3565b6
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895
Elucidation: A ‘Variable’ is a symbolic object that stands for a numerical defined ‘Mathematical’ object like e.g. a number, a vector, a matrix.
Example: x k
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_4ce76d7f_03f8_45b6_9003_90052a79bfaa
Elucidation: A ‘Mathematical’ that has no unknown value, i.e. all its ’Variable“-s parts refers to a ‘Number’ (for scalars that have a built-in datatype) or to another ‘Numerical’ (for complex numerical data structures that should rely on external implementations).
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0
Elucidation: The class of general mathematical symbolic objects respecting mathematical syntactic rules.
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_ae15fb4f_8e4d_41de_a0f9_3997f89ba6a2
Elucidation: A ‘varaible’ that stand for a well known constant.
Example: π refers to the constant number ~3.14
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_06658d8d_dcde_4fc9_aae1_17f71c0bcdec
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_fe7e56ce_118b_4243_9aad_20eb9f4f31f6
Elucidation: The dependent variable for which an equation has been written.
Example: Velocity, for the Navier-Stokes equation.
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_5be83f9c_a4ba_4b9a_be1a_5bfc6e891231
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_535d75a4_1972_40bc_88c6_ca566386934f
Elucidation: The equals symbol.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_b29fd350_39aa_4af7_9459_3faa0544cba6
Elucidation: A solvable set of one Physics Equation and one or more Materials Relations.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_6eca09be_17e9_445e_abc9_000aa61b7a11
Elucidation: A physics-based model based on a physics equation describing the behaviour of electrons.
Example: Density functional theory. Hartree-Fock.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_a4b14b83_9392_4a5f_a2e8_b2b58793f59b
Elucidation: A computational model that uses data to create new insight into the behaviour of a system.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_27c5d8c6_8af7_4d63_beb1_ec37cd8b3fa3
Elucidation: An ‘equation’ that stands for a ‘physical_law’ by mathematically defining the relations between physics_quantities.
Comment: The Newton’s equation of motion.
The Schrodinger equation.
The Navier-Stokes equation.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_53935db0_af45_4426_b9e9_244a0d77db00
Elucidation: A physics-based model based on a physics equation describing the behaviour of mesoscopic entities, i.e. a set of bounded atoms like a molecule, bead or nanoparticle.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_f7ed665b_c2e1_42bc_889b_6b42ed3a36f0
Comment: A mathematical model can be defined as a description of a system using mathematical concepts and language to facilitate proper explanation of a system or to study the effects of different components and to make predictions on patterns of behaviour.
Abramowitz and Stegun, 1968
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_4456a5d2_16a6_4ee1_9a8e_5c75956b28ea
Elucidation: A physics-based model based on a physics equation describing the behaviour of continuum volume.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_84cadc45_6758_46f2_ba2a_5ead65c70213
Elucidation: A physics-based model based on a physics equation describing the behaviour of atoms.
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_b5c58790_fb2d_42eb_b184_2a3f6ca60acb
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_707f0cd1_941c_4b57_9f20_d0ba30cd6ff3
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_3c424d37_cf62_41b1_ac9d_a316f8d113d6
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_8de14a59_660b_454f_aff8_76a07ce185f4
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_048a14e3_65fb_457d_8695_948965c89492
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_223d9523_4169_4ecd_b8af_acad1215e1ff
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_f8a2fe9f_458b_4771_9aba_a50e76afc52d
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_46d5643b_9706_4b67_8bea_ed77d6026539
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_f6d0c26a_98b6_4cf8_8632_aa259131faaa
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_2b1303e8_d4c3_453b_9918_76f1d009543f
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_a365b3c1_7bde_41d7_a15b_2820762e85f4
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_acd1a504_ca32_4f30_86ad_0b62cea5bc02
Elucidation: A reference unit provided by a reference material. International vocabulary of metrology (VIM)
Example: Arbitrary amount-of-substance concentration of lutropin in a given sample of plasma (WHO international standard 80/552): 5.0 International Unit/l
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_5ebd5e01_0ed3_49a2_a30d_cd05cbe72978
Elucidation: Represents the number 1, used as an explicit unit to say something has no units.
Example: Refractive index or volume fraction.
Example: Typically used for ratios of two units whos dimensions cancels out.
Qudtmatch: http://qudt.org/vocab/unit/UNITLESS
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_3ee80521_3c23_4dd1_935d_9d522614a3e2
Elucidation: A unit symbol that stands for a derived unit.
Example: Pa stands for N/m2 J stands for N m
Comment: Special units are semiotic shortcuts to more complex composed symbolic objects.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_50a3552e_859a_4ff7_946d_76d537cabce6
Elucidation: A symbol that stands for a concept in the language of the meterological domain of ISO 80000.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_216f448e_cdbc_4aeb_a529_7a5fe7fc38bb
Elucidation: A symbol that stands for a single unit.
Example: Some examples are “Pa”, “m” and “J”.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_18ce5200_00f5_45bb_8c6f_6fb128cd41ae
Comment: A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of such. International vocabulary of metrology (VIM)
Comment: A symbolic is recognized as reference unit also if it is not part of a quatity (e.g. as in the sentence “the Bq is the reference unit of Becquerel”).
For this reason we can’t declare the axiom: ReferenceUnit SubClassOf: inverse(hasReferenceUnit) some Quantity because there exist reference units without being part of a quantity.
This is peculiar to EMMO, where quantities (symbolic) are distinct with properties (semiotics).
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_985bec21_989f_4b9e_a4b3_735d88099c3c
Elucidation: A symbolic object used in metrology.
Comment: This language domain makes use of ISO 80000 concepts.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_32129fb5_df25_48fd_a29c_18a2f22a2dd5
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_c9c8f824_9127_4f93_bc21_69fe78a7f6f2
Elucidation: A reference unit provided by a measurement procedure.
Example: Rockwell C hardness of a given sample (150 kg load): 43.5HRC(150 kg)
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_db716151_6b73_45ff_910c_d182fdcbb4f5
Elucidation: A set of units that correspond to the base quantities in a system of units.
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_3ecff38b_b3cf_4a78_b49f_8580abf8715b
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_77e9dc31_5b19_463e_b000_44c6e79f98aa
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_e501069c_34d3_4dc7_ac87_c90c7342192b
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_af24ae20_8ef2_435a_86a1_2ea44488b318
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_9895a1b4_f0a5_4167_ac5e_97db40b8bfcc
Elucidation: A symbol that, following SI specifications, describe the physical dimensionality of a physical quantity and the exponents of the base units in a measurement unit.
Comment: All physical quantities, with the exception of counts, are derived quantities, which may be written in terms of base quantities according to the equations of physics. The dimensions of the derived quantities are written as products of powers of the dimensions of the base quantities using the equations that relate the derived quantities to the base quantities. In general the dimension of any quantity Q is written in the form of a dimensional product,
dim Q = T^α L^β M^γ I^δ Θ^ε N^ζ J^η
where the exponents α, β, γ, δ, ε, ζ and η, which are generally small integers, which can be positive, negative, or zero, are called the dimensional exponents. (SI brochure)
Comment: The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) type. The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity Q is denoted by dim Q. ISO 80000-1
Comment: The expression used by the EMMO for physical dimensions is a metrological symbol (but a string at meta level, i.e. the ontologist level) like this:
Ta Lb Mc Id Θe Nf Jg
where a, b, c, d, e, f and g are 0 or signed integers.
Regex for the physical dimension symbol for the EMMO is: ^T([+-][1-9]|0) L([+-][1-9]|0) M([+-][1-9]|0) I([+-][1-9]|0) Θ([+-][1-9]|0) N([+-][1-9]|0) J([+-][1-9]|0)$
Examples of correspondance between base units and physical dimensions are: mol -> T0 L0 M0 I0 Θ0 N+1 J0 s -> T+1 L0 M0 I0 Θ0 N0 J0 A/m2 -> T0 L0 M-2 I+1 Θ0 N0 J0
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_7610efb8_c7c6_4684_abc1_774783c62472
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_b14d9be5_f81e_469b_abca_379c2e83feab
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_b3600e73_3e05_479d_9714_c041c3acf5cc
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_ab79e92b_5377_454d_be06_d61b50db295a
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_3227b821_26a5_4c7c_9c01_5c24483e0bd0
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_ce7d4720_aa20_4a8c_93e8_df41a35b6723
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_d5f3e0e5_fc7d_4e64_86ad_555e74aaff84
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_a77a0a4b_6bd2_42b2_be27_4b63cebbb59e
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_321af35f_f0cc_4a5c_b4fe_8c2c0303fb0c
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_02e894c3_b793_4197_b120_3442e08f58d1
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_668e6ead_1530_40cc_ad5e_24b880edff50
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_f6070071_d054_4b17_9d2d_f446f7147d0f
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_5c003f53_20a2_4bd7_8445_58187e582578
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_2e7e5796_4a80_4d73_bb84_f31138446c0c
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_585e0ff0_9429_4d3c_b578_58abb1ba21d1
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_53e825d9_1a09_483c_baa7_37501ebfbe1c
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_ec903946_ddc9_464a_903c_7373e0d1eeb5
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_53bd0c90_41c3_46e2_8779_cd2a80f7e18b
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_501f9b3a_c469_48f7_9281_2e6a8d805d7a
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_515b5579_d526_4842_9e6f_ecc34db6f368
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_4f5c7c54_1c63_4d17_b12b_ea0792c2b187
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_14ff4393_0f28_4fb4_abc7_c2cc00bc761d
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_847f1d9f_205e_46c1_8cb6_a9e479421f88
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_4c49ab58_a6f6_409e_b849_f873ae1dcbee
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_c8d084ad_f88e_4596_8e4d_982c6655ce6f
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_bd67d149_24c2_4bc9_833a_c2bc26f98fd3
Elucidation: Increase in the rate of reaction of a specified chemical reaction that an enzyme produces in a specific assay system.
Iupacdoi: https://doi.org/10.1351/goldbook.C00881
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_cd2cd0de_e0cc_4ef1_b27e_2e88db027bac
Elucidation: Extend of a spatial dimension.
Dbpediamatch: http://dbpedia.org/page/Length
Iupacdoi: https://doi.org/10.1351/goldbook.L03498
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_3df10765_f6ff_4c9e_be3d_10b1809d78bd
Elucidation: A dose quantity used in the International Commission on Radiological Protection (ICRP) system of radiological protection.
Dbpediamatch: http://dbpedia.org/page/Energy
Iupacdoi: https://doi.org/10.1351/goldbook.E02101
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_66bc9029_f473_45ff_bab9_c3509ff37a22
Elucidation: An objective comparative measure of hot or cold.
Temperature is a relative quantity that can be used to express temperature differences. Unlike ThermodynamicTemperature, it cannot express absolute temperatures.
Dbpediamatch: http://dbpedia.org/page/Temperature
Iupacdoi: https://doi.org/10.1351/goldbook.T06261
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_02c0621e_a527_4790_8a0f_2bb51973c819
Elucidation: A ‘Mathematical’ entity that is made of a ‘Number’ and a ‘MeasurementUnit’ defined by a physical law, connected to a physical entity through a model perspective. Measurement is done according to the same model.
Comment: In the same system of quantities, dim ρB = ML−3 is the quantity dimension of mass concentration of component B, and ML−3 is also the quantity dimension of mass density, ρ. ISO 80000-1
Comment: Measured or simulated ‘physical propertiy’-s are always defined by a physical law, connected to a physical entity through a model perspective and measurement is done according to the same model.
Systems of units suggests that this is the correct approach, since except for the fundamental units (length, time, charge) every other unit is derived by mathematical relations between these fundamental units, implying a physical laws or definitions.
Comment: Measurement units of quantities of the same quantity dimension may be designated by the same name and symbol even when the quantities are not of the same kind.
For example, joule per kelvin and J/K are respectively the name and symbol of both a measurement unit of heat capacity and a measurement unit of entropy, which are generally not considered to be quantities of the same kind.
However, in some cases special measurement unit names are restricted to be used with quantities of specific kind only.
For example, the measurement unit ‘second to the power minus one’ (1/s) is called hertz (Hz) when used for frequencies and becquerel (Bq) when used for activities of radionuclides.
As another example, the joule (J) is used as a unit of energy, but never as a unit of moment of force, i.e. the newton metre (N · m).
Comment: — quantities of the same kind have the same quantity dimension, — quantities of different quantity dimensions are always of different kinds, and — quantities having the same quantity dimension are not necessarily of the same kind. ISO 80000-1
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_ffb73b1e_5786_43e4_a964_cb32ac7affb7
Elucidation: Measure of the ease for electric current to pass through a material.
Altlabel: Conductance
Comment: Inverse of ‘ElectricalResistance’.
Dbpediamatch: http://dbpedia.org/page/Electrical_resistance_and_conductance
Iupacdoi: https://doi.org/10.1351/goldbook.E01925
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_58a650f0_a638_4743_8439_535a325e5c4c
Elucidation: The magnitude of the electric charge carried by a single electron.
Comment: The DBpedia definition (http://dbpedia.org/page/Elementary_charge) is outdated as May 20, 2019. It is now an exact quantity.
Dbpediamatch: http://dbpedia.org/page/Elementary_charge
Iupacdoi: https://doi.org/10.1351/goldbook.E02032
Qudtmatch: http://physics.nist.gov/cuu/CODATA-Value_ElementaryCharge
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_99dba333_0dbd_4f75_8841_8c0f97fd58e2
Elucidation: The derivative of the electric charge of a system with respect to the electric potential.
Altlabel: ElectricCapacitance
Dbpediamatch: http://dbpedia.org/page/Capacitance
Iupacdoi: https://doi.org/10.1351/goldbook.C00791
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_31ec09ba_1713_42cb_83c7_b38bf6f9ced2
Elucidation: A property of objects which can be transferred to other objects or converted into different forms.
Comment: Energy is often defined as “ability of a system to perform work”, but it might be misleading since is not necessarily available to do work.
Dbpediamatch: http://dbpedia.org/page/Energy
Iupacdoi: https://doi.org/10.1351/goldbook.E02101
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_f3dd74c0_f480_49e8_9764_33b78638c235
Definition: Ratio of circular arc length to radius.
Dbpediamatch: http://dbpedia.org/page/Angle
Iupacdoi: https://doi.org/10.1351/goldbook.A00346
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_1f087811_06cb_42d5_90fb_25d0e7e068ef
Elucidation: Any interaction that, when unopposed, will change the motion of an object.
Dbpediamatch: http://dbpedia.org/page/Force
Iupacdoi: https://doi.org/10.1351/goldbook.F02480
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_8d3da9ac_2265_4382_bee5_db72046722f8
Elucidation: Decays per unit time.
Iupacdoi: https://doi.org/10.1351/goldbook.A00114
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_e88f75d6_9a17_4cfc_bdf7_43d7cea5a9a1
Elucidation: Measure of the difficulty to pass an electric current through a material.
Altlabel: Resistance
Comment: Inverse of ‘ElectricalConductance’.
Dbpediamatch: http://dbpedia.org/page/Electrical_resistance_and_conductance
Iupacdoi: https://doi.org/10.1351/goldbook.E01936
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_4f2d3939_91b1_4001_b8ab_7d19074bf845
Elucidation: Energy required to move a unit charge through an electric field from a reference point.
Altlabel: Voltage
Dbpediamatch: http://dbpedia.org/page/Voltage
Iupacdoi: https://doi.org/10.1351/goldbook.A00424
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_09b9021b_f97b_43eb_b83d_0a764b472bc2
Elucidation: Rate of transfer of energy per unit time.
Dbpediamatch: http://dbpedia.org/page/Power_(physics)
Iupacdoi: https://doi.org/10.1351/goldbook.P04792
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_2946d40b_24a1_47fa_8176_e3f79bb45064
Elucidation: Derived quantities defined in the International System of Quantities (ISQ).
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_e7c9f7fd_e534_4441_88fe_1fec6cb20f26
Elucidation: Ratio of area on a sphere to its radius squared.
Dbpediamatch: http://dbpedia.org/page/Solid_angle
Iupacdoi: https://doi.org/10.1351/goldbook.S05732
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_d4f7d378_5e3b_468a_baa1_a7e98358cda7
Elucidation: The indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.
Dbpediamatch: http://dbpedia.org/page/Time
Iupacdoi: https://doi.org/10.1351/goldbook.T06375
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_b51fbd00_a857_4132_9711_0ef70e7bdd20
Definition: The total luminous flux incident on a surface, per unit area.
Dbpediamatch: http://dbpedia.org/page/Illuminance
Iupacdoi: https://doi.org/10.1351/goldbook.I02941
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_3b931698_937e_49be_ab1b_36fa52d91181
Elucidation: Measure of magnetism, taking account of the strength and the extent of a magnetic field.
Dbpediamatch: http://dbpedia.org/page/Magnetic_flux
Iupacdoi: https://doi.org/10.1351/goldbook.M03684
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_f35cff4d_dc09_44cf_a729_22fb79e3bfb2
Elucidation: Quantities declared under the ISO 8000.
Seealso: https://www.iso.org/obp/ui/#iso:std:iso:80000:-1:ed-1:v1:en:sec:3.1
Wikipediaentry: https://en.wikipedia.org/wiki/International_System_of_Quantities
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_e2ee1c98_497a_4f66_b4ed_5711496a848e
Elucidation: Perceived power of light.
Dbpediamatch: http://dbpedia.org/page/Luminous_flux
Iupacdoi: https://doi.org/10.1351/goldbook.L03646
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_affe07e4_e9bc_4852_86c6_69e26182a17f
Elucidation: Thermodynamic temperature is the absolute measure of temperature. It is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point.
Dbpediamatch: http://dbpedia.org/page/Thermodynamic_temperature
Iupacdoi: https://doi.org/10.1351/goldbook.T06321
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_961d1aba_f75e_4411_aaa4_457f7516ed6b
Elucidation: Strength of the magnetic field.
Comment: Often denoted B.
Dbpediamatch: http://dbpedia.org/page/Magnetic_field
Iupacdoi: https://doi.org/10.1351/goldbook.M03686
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_ed4af7ae_63a2_497e_bb88_2309619ea405
Elucidation: Property of a physical body that express its resistance to acceleration (a change in its state of motion) when a force is applied.
Dbpediamatch: http://dbpedia.org/page/Mass
Iupacdoi: https://doi.org/10.1351/goldbook.M03709
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_f96feb3f_4438_4e43_aa44_7458c4d87fc2
Elucidation: The frequency standard in the SI system in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms are used to control the output frequency.
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_8e5dd473_808b_4a8a_b7cd_63068c12ff57
Definition: Energy imparted to matter by ionizing radiation in a suitable small element of volume divided by the mass of that element of volume.
Dbpediamatch: http://dbpedia.org/page/Absorbed_dose
Iupacdoi: https://doi.org/10.1351/goldbook.A00031
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_50a44256_9dc5_434b_bad4_74a4d9a29989
Elucidation: The force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Dbpediamatch: http://dbpedia.org/page/Pressure
Iupacdoi: https://doi.org/10.1351/goldbook.P04819
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_1a4c1a97_88a7_4d8e_b2f9_2ca58e92dde4
Elucidation: Base quantities defined in the International System of Quantities (ISQ).
Wikipediaentry: https://en.wikipedia.org/wiki/International_System_of_Quantities
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_852b4ab8_fc29_4749_a8c7_b92d4fca7d5a
Elucidation: Number of periods per time interval.
Dbpediamatch: http://dbpedia.org/page/Frequency
Iupacdoi: https://doi.org/10.1351/goldbook.FT07383
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_50bf79a6_a48b_424d_9d2c_813bd631231a
Elucidation: A measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle. It is based on the luminosity function, which is a standardized model of the sensitivity of the human eye.
Dbpediamatch: http://dbpedia.org/page/Luminous_intensity
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_1604f495_328a_4f28_9962_f4cc210739dd
Elucidation: The physical property of matter that causes it to experience a force when placed in an electromagnetic field.
Altlabel: Charge
Dbpediamatch: http://dbpedia.org/page/Electric_charge
Iupacdoi: https://doi.org/10.1351/goldbook.E01923
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_8159c26a_494b_4fa0_9959_10888f152298
Elucidation: The number of elementary entities present.
Dbpediamatch: http://dbpedia.org/page/Amount_of_substance
Iupacdoi: https://doi.org/10.1351/goldbook.A00297
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_c995ae70_3b84_4ebb_bcfc_69e6a281bb88
Elucidation: A flow of electric charge.
Dbpediamatch: http://dbpedia.org/page/Electric_current
Iupacdoi: https://doi.org/10.1351/goldbook.E01927
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_04cc9451_5306_45d0_8554_22cee4d6e785
Elucidation: A property of an electrical conductor by which a change in current through it induces an electromotive force in both the conductor itself and in any nearby conductors by mutual inductance.
Altlabel: ElectricInductance
Dbpediamatch: http://dbpedia.org/page/Inductance
Iupacdoi: https://doi.org/10.1351/goldbook.M04076
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_54dc83cb_06e1_4739_9e45_bc09cead7f48
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_f8bd64d5_5d3e_4ad4_a46e_c30714fecb7f
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_21f56795_ee72_4858_b571_11cfaa59c1a8
Elucidation: A numerical data value.
Comment: A number is actually a string (e.g. 1.4, 1e-8) of numerical digits and other symbols. However, in order not to increase complexity of the taxonomy and relations, here we take a number as an “atomic” object (i.e. we do not include digits in the EMMO as alphabet for numbers).
A ‘Number’ individual provide the link between the ontology and the actual data, through the data property hasNumericalValue.
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_18d180e4_5e3e_42f7_820c_e08951223486
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_8246541a_f1f6_4d03_8bd7_fc6b76d17375
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_707c6032_e272_4a20_98b5_d35c4f67be68
Comment: Derived units are defined as products of powers of the base units. When the numerical factor of this product is one, the derived units are called coherent derived units. The base and coherent derived units of the SI form a coherent set, designated the set of coherent SI units.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_5ebd5e01_0ed3_49a2_a30d_cd05cbe72978
Elucidation: Represents the number 1, used as an explicit unit to say something has no units.
Example: Refractive index or volume fraction.
Example: Typically used for ratios of two units whos dimensions cancels out.
Qudtmatch: http://qudt.org/vocab/unit/UNITLESS
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_feb03a8a_bbb6_4918_a891_46713ef557f4
Elucidation: The set of units provided by the SI referring to the ISQ.
Comment: The complete set of SI units includes both the coherent set and the multiples and sub-multiples formed by using the SI prefixes.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_3ee80521_3c23_4dd1_935d_9d522614a3e2
Elucidation: A unit symbol that stands for a derived unit.
Example: Pa stands for N/m2 J stands for N m
Comment: Special units are semiotic shortcuts to more complex composed symbolic objects.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_1273eb34_de48_43a9_925f_104110469dd2
Elucidation: A SI derived unit whos numerical factor in front of the product of SI base units is one.
Example: m/s kg/m^3
Comment: This class collects all units that are products or powers of SI base or SI special units only.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_b081b346_7279_46ef_9a3d_2c088fcd79f4
Elucidation: A ‘Quantity’ that stands for the standard reference magnitude of a specific class of measurement processes, defined and adopted by convention or by law.
The numerical quantity value of the ‘MeasurementUnit’ is conventionally 1 and does not appear.
Quantitative measurement results are expressed as a multiple of the ‘MeasurementUnit’.
Comment: “Real scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can be compared to express the ratio of the second quantity to the first one as a number” ISO 80000-1
Comment: “Unit symbols are mathematical entities and not abbreviations.”
“Symbols for units are treated as mathematical entities. In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra.”
https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf
Comment: While the SI brochure treats ‘MeasurementUnit’ as a ‘PhysicalQuantity’, in the EMMO this is not possible since the latter always has two direct parts, a ‘Numerical’ and a ‘MeasurementUnit’, while the former a single ‘Symbol’.
SI distinguishes between a quantity (an abstract concept) and the quantity value (a number and a reference). The EMMO, following strict nominalism, considers a SI quantity as a SI quantity value, collapsing the two concepts into one: the ‘Quantity’.
So, for the EMMO the symbol “kg” is not a physical quantity but a ‘MeasurementUnit’, while the string “1 kg” is ‘Physical Quantity’.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_216f448e_cdbc_4aeb_a529_7a5fe7fc38bb
Elucidation: A symbol that stands for a single unit.
Example: Some examples are “Pa”, “m” and “J”.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_d41ce84b_4317_41fb_a5d1_6cd281fca106
Elucidation: A SI base or special unit with a metric prefix.
Comment: The presence of the prefix makes this units non-coherent with SI system.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_08b308d4_31cd_4779_a784_aa92fc730f39
Elucidation: Derived units are defined as products of powers of the base units corresponding to the relations defining the derived quantities in terms of the base quantities.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_60b78cc3_6011_4134_95ab_956f56d4bdc1
Elucidation: A derived unit whos numerical factor in front of the product of base units is NOT equal to one.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_591e02fd_8d37_45a6_9d11_bb21cef391a0
Elucidation: A unit that does not belong to any system of units.
Example: eV barn
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_868ae137_4d25_493e_b270_21ea3d94849e
Elucidation: A measurement unit symbol that do not have a metric prefix as a direct spatial part.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_32129fb5_df25_48fd_a29c_18a2f22a2dd5
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_db716151_6b73_45ff_910c_d182fdcbb4f5
Elucidation: A set of units that correspond to the base quantities in a system of units.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_7db11dbf_a643_464a_9b56_07eabcc3e9c5
Definition: The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m s−1, where the second is defined in terms of ∆νCs.
Iupacdoi: https://doi.org/10.1351/goldbook.M03884
Qudtmatch: http://qudt.org/vocab/unit/M
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_2125f2d0_5050_49e3_a579_4c74bc9fd02e
Altlabel: A
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_42955b2d_b465_4666_86cc_ea3c2d685753
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_1e9c2a4b_abb9_4b27_bd9c_e31aac337a04
Altlabel: μ
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_ea192c80_6029_4410_863c_8eed7ea52037
Altlabel:
Comment: U+0020
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_cfcf0f48_09ac_4770_a06a_684a42b4a14c
Altlabel: a
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_e13b2173_1dec_4b97_9ac1_1dc4b418612a
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_db5dd38d_ac79_4af6_8782_fee7e7150ae8
Definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10−19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ∆νCs.
Iupacdoi: https://doi.org/10.1351/goldbook.A00300
Qudtmatch: http://qudt.org/vocab/unit/A
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_a3a701ed_6f7d_4a10_9aee_dfa1961fc7b7
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_aa0d5cde_cbdc_4815_b46d_2f76b00a6bde
Altlabel: m
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_2cfdcca6_6231_48aa_81b5_388b464bfe80
Altlabel: µ
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_9ff3bf8e_2168_406e_8251_1d158fc948ae
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_7db11dbf_a643_464a_9b56_07eabcc3e9c5
Definition: The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m s−1, where the second is defined in terms of ∆νCs.
Iupacdoi: https://doi.org/10.1351/goldbook.M03884
Qudtmatch: http://qudt.org/vocab/unit/M
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_db5dd38d_ac79_4af6_8782_fee7e7150ae8
Definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10−19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ∆νCs.
Iupacdoi: https://doi.org/10.1351/goldbook.A00300
Qudtmatch: http://qudt.org/vocab/unit/A
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_9bfd6f1e_b0ce_459c_beb7_8f1f41708bba
Definition: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J s, which is equal to kg m2 s−1, where the metre and the second are defined in terms of c and ∆νCs.
Iupacdoi: https://doi.org/10.1351/goldbook.K03391
Qudtmatch: http://qudt.org/vocab/unit/KiloGM
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_314ba716_2d3d_4462_9a4f_d3419ae1df43
Definition: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.
Iupacdoi: https://doi.org/10.1351/goldbook.S05513
Qudtmatch: http://qudt.org/vocab/unit/SEC
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_2e5e45fc_f52c_4294_bdc2_5ed7a06dfce7
Definition: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380649×10−23 when expressed in the unit J K−1, which is equal to kg m2 s−2 K−1, where the kilogram, metre and second are defined in terms of h, c and ∆νCs.
Iupacdoi: https://doi.org/10.1351/goldbook.K03374
Qudtmatch: http://qudt.org/vocab/unit/K
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_df6eeb01_1b41_4bd8_9257_a04fbd7cf000
Definition: The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.
Iupacdoi: https://doi.org/10.1351/goldbook.M03980
Qudtmatch: http://qudt.org/vocab/unit/MOL
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_3a185e6c_9e19_4776_b583_19c978156aa0
Elucidation: The base units in the SI system.
Seealso: https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_8d00f093_3f45_4ea3_986c_b3545c3c2f4c
Definition: The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed in the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ∆νCs.
Iupacdoi: https://doi.org/10.1351/goldbook.C00787
Qudtmatch: http://qudt.org/vocab/unit/CD
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_acb50123_87a2_4753_b36c_f87114ad4de2
Comment: Measurement unit for magnetic flux density or induction.
Iupacdoi: https://doi.org/10.1351/goldbook.T06283
Qudtmatch: http://qudt.org/vocab/unit/T
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_696ed548_9477_45ea_993c_6a8f5271914a
Comment: Measurement unit for electric charge.
Iupacdoi: https://doi.org/10.1351/goldbook.C01365
Qudtmatch: http://qudt.org/vocab/unit/C
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_dc232f53_8ed8_4ddd_9f41_cc057985eadb
Comment: Measurement unit for equivalent doseof ionizing radiation.
Sievert is derived from absorbed dose, but takes into account the biological effectiveness of the radiation, which is dependent on the radiation type and energy.
Iupacdoi: https://doi.org/10.1351/goldbook.S05658
Qudtmatch: http://qudt.org/vocab/unit/SV
Wikipediaentry: https://en.wikipedia.org/wiki/Equivalent_dose
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_080052a1_f295_44be_a60f_1326ce13f1ba
Comment: Measurement unit for power.
Iupacdoi: https://doi.org/10.1351/goldbook.W06656
Qudtmatch: http://qudt.org/vocab/unit/W
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_59c10c5c_47bd_4348_ba39_38836607dfa1
Comment: Measurement unit for resistance.
Iupacdoi: https://doi.org/10.1351/goldbook.O04280
Qudtmatch: http://qudt.org/vocab/unit/OHM
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_00199e76_69dc_45b6_a9c6_98cc90cdc0f5
Comment: Measurement unit for absorbed dose.
Iupacdoi: https://doi.org/10.1351/goldbook.G02696
Qudtmatch: http://qudt.org/vocab/unit/GRAY
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_8a70dea4_d6ab_4260_b931_a3e990982416
Comment: Measurement unit for energy.
Iupacdoi: https://doi.org/10.1351/goldbook.J03363
Qudtmatch: http://qudt.org/vocab/unit/J
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_cf3dd6cc_c5d6_4b3d_aef4_82f3b7a361af
Elucidation: Dimensionless measurement unit for solid angle.
Iupacdoi: https://doi.org/10.1351/goldbook.S05971
Qudtmatch: http://qudt.org/vocab/unit/SR
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_e9ffc696_5228_4ff9_8a60_0f5e05e9931b
Elucidation: The 22 derived units that are given a special name in the SI system that stands for units derived by SI base units.
Comment: These units are SI coherent by definition.
Wikipediaentry: https://en.wikipedia.org/wiki/International_System_of_Units#Derived_units
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_fab003c8_f7a6_4346_9988_7161325ed7a3
Comment: Measurement unit for electrical inductance.
Iupacdoi: https://doi.org/10.1351/goldbook.H02782
Qudtmatch: http://qudt.org/vocab/unit/H
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_b71e4ba5_8f73_4199_8c96_7ea7f94d9e2a
Definition: Radioactive decays per second.
Comment: Unit for radioactive activity.
Iupacdoi: https://doi.org/10.1351/goldbook.B00624
Qudtmatch: http://qudt.org/vocab/unit/BQ
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_f2523820_04a6_44ab_bb67_8237dda2b0c2
Comment: Measurement unit for electrical conductance.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_a979c531_f9fa_4a6e_93c1.0.0-alpha960241ca6
Comment: Measurement unit for force.
Iupacdoi: https://doi.org/10.1351/goldbook.N04135
Qudtmatch: http://qudt.org/vocab/unit/N
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_33b67e69_3645_4c73_b100_5ea6759221b4
Comment: Measurement unit for catalytic activity.
Iupacdoi: https://doi.org/10.1351/goldbook.K03372
Qudtmatch: http://qudt.org/vocab/unit/KAT
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_a9201b2f_e6de_442a_b3a6_d291.0.0-alphaa582
Comment: Measurement unit for electric capacitance.
Iupacdoi: https://doi.org/10.1351/goldbook.F02320
Qudtmatch: http://qudt.org/vocab/unit/FARAD
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_da1dd4a7_c611_4ad4_bef6_7646f28aa598
Comment: Measurement unit for illuminance.
Iupacdoi: https://doi.org/10.1351/goldbook.L03651
Qudtmatch: http://qudt.org/vocab/unit/LUX
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_d7f11b34_a121_4519_87c0_aa754f1c4737
Comment: Measurement unit for magnetic flux.
Iupacdoi: https://doi.org/10.1351/goldbook.W06666
Qudtmatch: http://qudt.org/vocab/unit/WB
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_e2207e91_02b0_4a8a_b13e_61d2a2a839f1
Comment: Measurement unit for voltage.
Iupacdoi: https://doi.org/10.1351/goldbook.V06634
Qudtmatch: http://qudt.org/vocab/unit/V
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_d7b7fd1e_645a_42cb_8f40_85f0d034d3ae
Comment: Measurement unit for luminous flux.
Iupacdoi: https://doi.org/10.1351/goldbook.L03639
Qudtmatch: http://qudt.org/vocab/unit/LM
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_e75f580e_52bf_4dd5_af70_df409cec08fd
Comment: Measurement unit for frequence.
Iupacdoi: https://doi.org/10.1351/goldbook.H02785
Qudtmatch: http://qudt.org/vocab/unit/HZ
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_a121bb1d_5225_4c78_809b_0268c3012208
Elucidation: Measure of plane angle.
Comment: Dimensionless measurement unit for plane angle.
Iupacdoi: https://doi.org/10.1351/goldbook.R05036
Qudtmatch: http://qudt.org/vocab/unit/RAD
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_a80dc6f5_b1aa_41a7_a3a8_cd5040da2162
Comment: Measurement unit for pressure.
Iupacdoi: https://doi.org/10.1351/goldbook.P04442
Qudtmatch: http://qudt.org/vocab/unit/PA
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_b20be325_8bfd_4237_bee7_201ab0fd9c75
Comment: Measurement unit for Celsius temperature. This unit can only be used for expressing temperature differences.
Iupacdoi: https://doi.org/10.1351/goldbook.D01561
Qudtmatch: http://qudt.org/vocab/unit/DEG_C
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_c6d4a5e0_7e95_44df_a6db_84ee0a8bbc8e
Elucidation: A measurement unit that is made of a metric prefix and a unit symbol.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_a2f94f33_71fa_443c_a1fb_d1685fc537ec
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_d41ce84b_4317_41fb_a5d1_6cd281fca106
Elucidation: A SI base or special unit with a metric prefix.
Comment: The presence of the prefix makes this units non-coherent with SI system.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_62f0d847_3603_45b4_bfc4_dd4511355ff2
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_e1981c25_7c55_4020_aa7a_d2e14ced86d4
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_254472c6_3dbd_4f02_bc43_571389cd281f
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_068c4e58_2470_4b1c_8454_010dd4906100
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_5eaecadc_4f0d_4a3a_afc7_1fc0b83cc928
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_23bfe79a_cade_48f1_9a8c_fd96e6bac8ba
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_471cb92b_edca_4cf9_bce8_a75084d876b8
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_5cf9f86c_86f5_40c4_846d_60371f670e0a
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_21aaefc1_3f86_4208_b7db_a755f31f0f8c
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_7d2afa66_ae9e_4095_a9bf_421d0be401b6
Elucidation: Dimensionless multiplicative unit prefix.
Seealso: https://en.wikipedia.org/wiki/Metric_prefix
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_1d8b370b_c672_4d0c_964e_eaafcbf2f51f
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_daa9ee97_4c5f_42e5_918c_44d7523e8958
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_43a6b269_da31_4bb6_a537_c97df4fff32a
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_1181c938_c8f0_4ad6_bc7a_2bfdc0903d29
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_42955b2d_b465_4666_86cc_ea3c2d685753
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_f5769206_9257_4b08_bf7b_dad7868c6afc
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_3a204900_2b33_47d1_b444_815cc4c8cffa
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_74931b1b_c133_4e59_9a75_1bf0e1626201
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_e79c62ff_10ad_4ec0_baba_c19ddd4eaa11
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_a3a701ed_6f7d_4a10_9aee_dfa1961fc7b7
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_a8eb4bbb_1bd3_4ad4_b114_2789bcbd2134
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_b55cd09a_e54d_4eb1_81dd_03c29d1b878e
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_9ff3bf8e_2168_406e_8251_1d158fc948ae
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_c46f091c_0420_4c1a_af30_0a2c8ebcf7d7
Elucidation: “Quantity, defined by a conventional measurement procedure, for which a total ordering relation can be established, according to magnitude, with other quantities of the same kind, but for which no algebraic operations among those quantities exist” International vocabulary of metrology (VIM)
Example: Hardness Resilience
Comment: “Ordinal quantities, such as Rockwell C hardness, are usually not considered to be part of a system of quantities because they are related to other quantities through empirical relations only.” International vocabulary of metrology (VIM)
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_d8aa8e1f_b650_416d_88a0_5118de945456
Elucidation: A quantitative property attributed by agreement to a quantity for a given purpose.
Example: The thermal conductivity of a copper sample in my laboratory can be assumed to be the conductivity that appears in the vendor specification. This value has been obtained by measurement of a sample which is not the one I have in my laboratory. This conductivity value is then a conventional quantitiative property assigned to my sample through a semiotic process in which no actual measurement is done by my laboratory.
If I don’t believe the vendor, then I can measure the actual thermal conductivity. I then perform a measurement process that semiotically assign another value for the conductivity, which is a measured property, since is part of a measurement process.
Then I have two different physical quantities that are properties thanks to two different semiotic processes.
Comment: A property that is associated to an object by convention, or assumption.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_f658c301_ce93_46cf_9639_4eace2c5d1d5
Elucidation: A symbolic that has parts a reference unit and a numerical object separated by a space expressing the value of a quantitative property (expressed as the product of the numerical and the unit).
Example: 6.8 m 0.9 km 8 K 6 MeV 43.5 HRC(150 kg)
Comment: A quantity is not necessarily a property, since it is possible to write “10 kg”, without assigning this quantity to a specific object.
However, a quantitative property is always a quantity.
Comment: Referred as Quantity Value in International vocabulary of metrology (VIM)
Comment: SI distinguishes between a quantity (an abstract concept) and the quantity value (a number and a reference).
The EMMO, following strict nominalism, denies the existence of abstract objects and then collapses the two concepts of SI quantity and SI quantity value into a single one: the ‘Quantity’.
So, for the EMMO the symbol “kg” is not a physical quantity but simply a ‘Symbolic’ object categorized as a ‘MeasurementUnit’.
While the string “1 kg” is a ‘Physical Quantity’.
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_d0200cf1_e4f4_45ae_873f_b9359daea3cd
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_873b0ab3_88e6_4054_b901_5531e01f14a4
Relations:
IRI: http://emmo.info/emmo/middle/properties#EMMO_dd4a7f3e_ef56_466c_ac1a_d2716b5f87ec
Elucidation: A ‘Quantity’ that can be quantified with respect to a standardized reference physical instance (e.g. the prototype meter bar, the kg prototype) or method (e.g. resilience) through a measurement process.
Comment: “A property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by means of a number and a reference” ISO 80000-1
“A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of such.” International vocabulary of metrology (VIM)
Comment: A quantitative property is always expresssed as a quantity (i.e. a number and a reference unit). For the EMMO, a nominalistic ontology, there is no property as abstract object.
A property is a sign that stands for an object according to a specific code shared by some observers.
For quantititative properties, one possible code that is shared between the scientific community (the observers) is the SI system of units.
Comment: Subclasses of ‘QuantitativeProperty’ classify objects according to the type semiosis that is used to connect the property to the object (e.g. by measurement, by convention, by modelling).
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_ed4af7ae_63a2_497e_bb88_2309619ea405
Elucidation: Property of a physical body that express its resistance to acceleration (a change in its state of motion) when a force is applied.
Dbpediamatch: http://dbpedia.org/page/Mass
Iupacdoi: https://doi.org/10.1351/goldbook.M03709
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_cd2cd0de_e0cc_4ef1_b27e_2e88db027bac
Elucidation: Extend of a spatial dimension.
Dbpediamatch: http://dbpedia.org/page/Length
Iupacdoi: https://doi.org/10.1351/goldbook.L03498
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_d4f7d378_5e3b_468a_baa1_a7e98358cda7
Elucidation: The indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.
Dbpediamatch: http://dbpedia.org/page/Time
Iupacdoi: https://doi.org/10.1351/goldbook.T06375
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_1a4c1a97_88a7_4d8e_b2f9_2ca58e92dde4
Elucidation: Base quantities defined in the International System of Quantities (ISQ).
Wikipediaentry: https://en.wikipedia.org/wiki/International_System_of_Quantities
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_acaaa124_3dde_48b6_86e6_6ec6f364f408
Elucidation: “Quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the subset can be expressed in terms of the other quantities within that subset” ISO 80000-1
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_50bf79a6_a48b_424d_9d2c_813bd631231a
Elucidation: A measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle. It is based on the luminosity function, which is a standardized model of the sensitivity of the human eye.
Dbpediamatch: http://dbpedia.org/page/Luminous_intensity
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_affe07e4_e9bc_4852_86c6_69e26182a17f
Elucidation: Thermodynamic temperature is the absolute measure of temperature. It is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point.
Dbpediamatch: http://dbpedia.org/page/Thermodynamic_temperature
Iupacdoi: https://doi.org/10.1351/goldbook.T06321
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_8159c26a_494b_4fa0_9959_10888f152298
Elucidation: The number of elementary entities present.
Dbpediamatch: http://dbpedia.org/page/Amount_of_substance
Iupacdoi: https://doi.org/10.1351/goldbook.A00297
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_c995ae70_3b84_4ebb_bcfc_69e6a281bb88
Elucidation: A flow of electric charge.
Dbpediamatch: http://dbpedia.org/page/Electric_current
Iupacdoi: https://doi.org/10.1351/goldbook.E01927
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_2946d40b_24a1_47fa_8176_e3f79bb45064
Elucidation: Derived quantities defined in the International System of Quantities (ISQ).
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_bd67d149_24c2_4bc9_833a_c2bc26f98fd3
Elucidation: Increase in the rate of reaction of a specified chemical reaction that an enzyme produces in a specific assay system.
Iupacdoi: https://doi.org/10.1351/goldbook.C00881
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_e7c9f7fd_e534_4441_88fe_1fec6cb20f26
Elucidation: Ratio of area on a sphere to its radius squared.
Dbpediamatch: http://dbpedia.org/page/Solid_angle
Iupacdoi: https://doi.org/10.1351/goldbook.S05732
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_3df10765_f6ff_4c9e_be3d_10b1809d78bd
Elucidation: A dose quantity used in the International Commission on Radiological Protection (ICRP) system of radiological protection.
Dbpediamatch: http://dbpedia.org/page/Energy
Iupacdoi: https://doi.org/10.1351/goldbook.E02101
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_71f6ab56_342c_484b_bbe0_de86b7367cb3
Elucidation: “Quantity, in a system of quantities, defined in terms of the base quantities of that system”.
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_b51fbd00_a857_4132_9711_0ef70e7bdd20
Definition: The total luminous flux incident on a surface, per unit area.
Dbpediamatch: http://dbpedia.org/page/Illuminance
Iupacdoi: https://doi.org/10.1351/goldbook.I02941
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_3b931698_937e_49be_ab1b_36fa52d91181
Elucidation: Measure of magnetism, taking account of the strength and the extent of a magnetic field.
Dbpediamatch: http://dbpedia.org/page/Magnetic_flux
Iupacdoi: https://doi.org/10.1351/goldbook.M03684
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_e2ee1c98_497a_4f66_b4ed_5711496a848e
Elucidation: Perceived power of light.
Dbpediamatch: http://dbpedia.org/page/Luminous_flux
Iupacdoi: https://doi.org/10.1351/goldbook.L03646
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_66bc9029_f473_45ff_bab9_c3509ff37a22
Elucidation: An objective comparative measure of hot or cold.
Temperature is a relative quantity that can be used to express temperature differences. Unlike ThermodynamicTemperature, it cannot express absolute temperatures.
Dbpediamatch: http://dbpedia.org/page/Temperature
Iupacdoi: https://doi.org/10.1351/goldbook.T06261
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_ffb73b1e_5786_43e4_a964_cb32ac7affb7
Elucidation: Measure of the ease for electric current to pass through a material.
Altlabel: Conductance
Comment: Inverse of ‘ElectricalResistance’.
Dbpediamatch: http://dbpedia.org/page/Electrical_resistance_and_conductance
Iupacdoi: https://doi.org/10.1351/goldbook.E01925
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_58a650f0_a638_4743_8439_535a325e5c4c
Elucidation: The magnitude of the electric charge carried by a single electron.
Comment: The DBpedia definition (http://dbpedia.org/page/Elementary_charge) is outdated as May 20, 2019. It is now an exact quantity.
Dbpediamatch: http://dbpedia.org/page/Elementary_charge
Iupacdoi: https://doi.org/10.1351/goldbook.E02032
Qudtmatch: http://physics.nist.gov/cuu/CODATA-Value_ElementaryCharge
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_99dba333_0dbd_4f75_8841_8c0f97fd58e2
Elucidation: The derivative of the electric charge of a system with respect to the electric potential.
Altlabel: ElectricCapacitance
Dbpediamatch: http://dbpedia.org/page/Capacitance
Iupacdoi: https://doi.org/10.1351/goldbook.C00791
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_31ec09ba_1713_42cb_83c7_b38bf6f9ced2
Elucidation: A property of objects which can be transferred to other objects or converted into different forms.
Comment: Energy is often defined as “ability of a system to perform work”, but it might be misleading since is not necessarily available to do work.
Dbpediamatch: http://dbpedia.org/page/Energy
Iupacdoi: https://doi.org/10.1351/goldbook.E02101
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_961d1aba_f75e_4411_aaa4_457f7516ed6b
Elucidation: Strength of the magnetic field.
Comment: Often denoted B.
Dbpediamatch: http://dbpedia.org/page/Magnetic_field
Iupacdoi: https://doi.org/10.1351/goldbook.M03686
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_f3dd74c0_f480_49e8_9764_33b78638c235
Definition: Ratio of circular arc length to radius.
Dbpediamatch: http://dbpedia.org/page/Angle
Iupacdoi: https://doi.org/10.1351/goldbook.A00346
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_f96feb3f_4438_4e43_aa44_7458c4d87fc2
Elucidation: The frequency standard in the SI system in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms are used to control the output frequency.
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_1f087811_06cb_42d5_90fb_25d0e7e068ef
Elucidation: Any interaction that, when unopposed, will change the motion of an object.
Dbpediamatch: http://dbpedia.org/page/Force
Iupacdoi: https://doi.org/10.1351/goldbook.F02480
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_8e5dd473_808b_4a8a_b7cd_63068c12ff57
Definition: Energy imparted to matter by ionizing radiation in a suitable small element of volume divided by the mass of that element of volume.
Dbpediamatch: http://dbpedia.org/page/Absorbed_dose
Iupacdoi: https://doi.org/10.1351/goldbook.A00031
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_50a44256_9dc5_434b_bad4_74a4d9a29989
Elucidation: The force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Dbpediamatch: http://dbpedia.org/page/Pressure
Iupacdoi: https://doi.org/10.1351/goldbook.P04819
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_8d3da9ac_2265_4382_bee5_db72046722f8
Elucidation: Decays per unit time.
Iupacdoi: https://doi.org/10.1351/goldbook.A00114
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_852b4ab8_fc29_4749_a8c7_b92d4fca7d5a
Elucidation: Number of periods per time interval.
Dbpediamatch: http://dbpedia.org/page/Frequency
Iupacdoi: https://doi.org/10.1351/goldbook.FT07383
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_1604f495_328a_4f28_9962_f4cc210739dd
Elucidation: The physical property of matter that causes it to experience a force when placed in an electromagnetic field.
Altlabel: Charge
Dbpediamatch: http://dbpedia.org/page/Electric_charge
Iupacdoi: https://doi.org/10.1351/goldbook.E01923
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_e88f75d6_9a17_4cfc_bdf7_43d7cea5a9a1
Elucidation: Measure of the difficulty to pass an electric current through a material.
Altlabel: Resistance
Comment: Inverse of ‘ElectricalConductance’.
Dbpediamatch: http://dbpedia.org/page/Electrical_resistance_and_conductance
Iupacdoi: https://doi.org/10.1351/goldbook.E01936
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_4f2d3939_91b1_4001_b8ab_7d19074bf845
Elucidation: Energy required to move a unit charge through an electric field from a reference point.
Altlabel: Voltage
Dbpediamatch: http://dbpedia.org/page/Voltage
Iupacdoi: https://doi.org/10.1351/goldbook.A00424
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_09b9021b_f97b_43eb_b83d_0a764b472bc2
Elucidation: Rate of transfer of energy per unit time.
Dbpediamatch: http://dbpedia.org/page/Power_(physics)
Iupacdoi: https://doi.org/10.1351/goldbook.P04792
Relations:
IRI: http://emmo.info/emmo/middle/isq#EMMO_04cc9451_5306_45d0_8554_22cee4d6e785
Elucidation: A property of an electrical conductor by which a change in current through it induces an electromotive force in both the conductor itself and in any nearby conductors by mutual inductance.
Altlabel: ElectricInductance
Dbpediamatch: http://dbpedia.org/page/Inductance
Iupacdoi: https://doi.org/10.1351/goldbook.M04076
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_ffc7735f_c177_46a4_98e9_a54440d29209
Elucidation: A physical constant relating energy at the individual particle level with temperature. It is the gas constant R divided by the Avogadro constant.
Comment: The DBpedia definition (http://dbpedia.org/page/Boltzmann_constant) is outdated as May 20, 2019. It is now an exact quantity.
Dbpediamatch: http://dbpedia.org/page/Boltzmann_constant
Iupacdoi: https://doi.org/10.1351/goldbook.B00695
Qudtmatch: http://physics.nist.gov/cuu/CODATA-Value_BoltzmannConstant
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_f96feb3f_4438_4e43_aa44_7458c4d87fc2
Elucidation: The frequency standard in the SI system in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms are used to control the output frequency.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_76cc4efc_231e_42b4_be83_2547681caed6
Elucidation: The quantum of action.
Dbpediamatch: http://dbpedia.org/page/Planck_constant
Iupacdoi: https://doi.org/10.1351/goldbook.P04685
Qudtmatch: http://physics.nist.gov/cuu/CODATA-Value_PlankConstant
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_99296e55_53f7_4333_9e06_760ad175a1b9
Elucidation: The speed of light in vacuum.
Dbpediamatch: http://dbpedia.org/page/Speed_of_light
Iupacdoi: https://doi.org/10.1351/goldbook.S05854
Qudtmatch: http://physics.nist.gov/cuu/CODATA-Value_SpeedOfLightInVacuum
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_176cae33_b83e_4cd2_a6bc_281f42f0ccc8
Elucidation: The number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole.
Comment: The DBpedia definition (http://dbpedia.org/page/Avogadro_constant) is outdated as May 20, 2019. It is now an exact quantity.
Dbpediamatch: http://dbpedia.org/page/Avogadro_constant
Iupacdoi: https://doi.org/10.1351/goldbook.A00543
Qudtmatch: http://physics.nist.gov/cuu/CODATA-Value_AvogadroConstant
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_3f15d200_c97b_42c8_8ac0_d81d150361e2
Elucidation: For a given unit system, measured constants are physical constants that are not used to define the unit system. Hence, these constants have to be measured and will therefore be associated with an uncertainty.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_58a650f0_a638_4743_8439_535a325e5c4c
Elucidation: The magnitude of the electric charge carried by a single electron.
Comment: The DBpedia definition (http://dbpedia.org/page/Elementary_charge) is outdated as May 20, 2019. It is now an exact quantity.
Dbpediamatch: http://dbpedia.org/page/Elementary_charge
Iupacdoi: https://doi.org/10.1351/goldbook.E02032
Qudtmatch: http://physics.nist.gov/cuu/CODATA-Value_ElementaryCharge
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_b953f2b1_c8d1_4dd9_b630_d3ef6580c2bb
Comment: Physical constants are categorised into “exact” and measured constants.
With “exact” constants, we refer to physical constants that have an exact numerical value after the revision of the SI system that was enforsed May 2019.
Wikipediaentry: https://en.wikipedia.org/wiki/List_of_physical_constants
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_506f7823_52bc_40cb_be07_b3b1e10cce13
Elucidation: The luminous efficacy of monochromatic radiation of frequency 540 × 10 12 Hz, K cd , is a technical constant that gives an exact numerical relationship between the purely physical characteristics of the radiant power stimulating the human eye (W) and its photobiological response defined by the luminous flux due to the spectral responsivity of a standard observer (lm) at a frequency of 540 × 10 12 hertz.
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_f2ca6dd0_0e5f_4392_a92d_cafdae6cfc95
Elucidation: Physical constant that by definition (after the latest revision of the SI system that was enforsed May 2019) has a known exact numerical value when expressed in SI units.
Relations:
IRI: http://emmo.info/emmo/middle/metrology#EMMO_89762966_8076_4f7c_b745_f718d653e8e2
Comment: Physical constant used to define a unit system. Hence, when expressed in that unit system they have an exact value with no associated uncertainty.
Relations:
IRI: http://emmo.info/emmo/middle/reductionistic#EMMO_52211e5e_d767_4812_845e_eb6b402c476a
Elucidation: A ‘Physical’ which is a tessellation of ‘State’ temporal direct parts.
Comment: ‘Existent’ is the EMMO class to be used for representing real world physical objects under a reductionistic perspective (i.e. objects come from the composition of sub-part objects, both in time and space).
‘Existent’ class collects all individuals that stand for physical objects that can be structured in well defined temporal sub-parts called states, through the temporal direct parthood relation.
This class provides a first granularity hierarchy in time, and a way to axiomatize tessellation principles for a specific whole with a non-transitivity relation (direct parthood) that helps to retain the granularity levels.
e.g. a car, a supersaturated gas with nucleating nanoparticles, an atom that becomes ionized and then recombines with an electron.
Comment: An ‘Existent’ individual stands for a real world object for which the ontologist can provide univocal tessellation in time.
By definition, the tiles are represented by ‘State’-s individual.
Tiles are related to the ‘Existent’ through temporal direct parthood, enforcing non-transitivity and inverse-functionality.
Comment: Being hasTemporalDirectPart a proper parthood relation, there cannot be ‘Existent’ made of a single ‘State’.
Moreover, due to inverse functionality, a ‘State’ can be part of only one ‘Existent’, preventing overlapping between ‘Existent’-s.
Comment: ex-sistere (latin): to stay (to persist through time) outside others of the same type (to be distinct from the rest).
Relations:
IRI: http://emmo.info/emmo/middle/reductionistic#EMMO_15db234d_ecaf_4715_9838_4b4ec424fb13
Elucidation: A class devoted to categorize ‘Physical’-s according to their granularity relations, first in terms of time evolution (Existent) and then in terms of their composition (State), up to the spatial a-tomistic element (Elementary).
Direct parthood is the relation used to build the class hierarchy (and the granularity hierarchy).
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_89a0c87c_0804_4013_937a_6fe234d9499c
Elucidation: A symbolic entity made of other symbolic entities according to a specific spatial configuration.
Relations:
IRI: http://emmo.info/emmo/middle/reductionistic#EMMO_36c79456_e29c_400d_8bd3_0eedddb82652
Elucidation: A ‘Physical’ which is a tessellation of spatial direct parts.
Example: e.g. the existent in my glass is declared at t = t_start as made of two direct parts: the ice and the water. It will continue to exists as state as long as the ice is completely melt at t = t_end. The new state will be completely made of water. Between t_start and t_end there is an exchange of molecules between the ice and the water, but this does not affect the existence of the two states.
If we partition the existent in my glass as ice surrounded by several molecules (we do not use the object water as direct part) then the appearance of a molecule coming from the ice will cause a state to end and another state to begin.
Comment: Direct partitions declaration is a choice of the ontologist that choses the classes to be used as direct parts, according to its own world view.
A ‘State’ can always be direct partitioned in ‘Elementary’-s and ‘Void’ or ‘Physical’.
e.g. the water in my glass can be seen as a single object without declaring direct parts, or as made of H2O molecules direct parts.
Comment: The definition of ‘State’ implies that its spatial direct parts (i.e. ‘physicals’) are not gained or lost during its temporal extension (they exist from the left to the right side of the time interval), so that the cardinality of spatial direct parts in a ‘State’ is constant.
This does not mean that there cannot be a change in the internal structure of the ‘State’ direct parts. It means only that this change must not affect the existence of the direct part itself.
There is no change in granularity or cardinality of direct parts of a ‘State’.
The use of spatial direct parthood in ‘State’ definition means that a ‘State’ cannot overlap in space another ‘State’.
Comment: The usefulness of ‘State’ is that it makes it possible to describe the evolution in time of an ‘Existent’ in terms of series of ‘State’-s that can take into account the disappearance or appearance of parts within a ‘Physical’.
A ‘State’ is a recognizable granularity level of matter, in the sense that its direct parts do not appear or disappear within its lifetime as it can be for a generic ‘Existent’.
Comment: There is no change in granularity or cardinality of parts within a state.
The use of spatial direct parthood in state definition means that a state cannot overlap in space another state that is direct part of the same whole.
Relations:
IRI: http://emmo.info/emmo/middle/perceptual#EMMO_50ea1ec5_f157_41b0_b46b_a9032f17ca10
Elucidation: A physical made of more than one symbol sequentially arranged.
Example: The word “cat” considered as a collection of ‘symbol’-s respecting the rules of english language.
In this example the ‘symbolic’ entity “cat” is not related to the real cat, but it is only a word (like it would be to an italian person that ignores the meaning of this english word).
If an ‘interpreter’ skilled in english language is involved in a ‘semiotic’ process with this word, that “cat” became also a ‘sign’ i.e. it became for the ‘interpreter’ a representation for a real cat.
Comment: A string is made of concatenated symbols whose arrangement is one-dimensional. Each symbol can have only one previous and one next neighborhood (bidirectional list).
Comment: A string is not requested to respect any syntactic rule: it’s simply directly made of symbols.
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_89083bab_f69c_4d06_bf6d_62973b56cdc7
Example: 2+2
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_f9bc8b52_85e9_4b53_b969_dd7724d5b8e4
Elucidation: A well-formed finite combination of mathematical symbols according to some specific rules.
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_91447ec0_fb55_49f2_85a5_3172dff6482c
Example: 2 * x^2 + x + 3
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_1aed91a3_d00c_48af_8f43_a0c958b2512a
Example: 2x+3
Comment: An expression that has parts only integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_98d65021_4574_4890_b2fb_46430841077f
Example: 2 * a - b = c
Comment: An ‘equation’ that has parts two ‘polynomial’-s
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_a6138ba7_e365_4f2d_b6b4_fe5a5918d403
Example: 1 + 1 = 2
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_0b6ebe5a_0026_4bef_a1c1_5be00df9f98e
Elucidation: A relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Example: f(x) > 0
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_29afdf54_90ae_4c98_8845_fa9ea3f143a8
Elucidation: An equation that define a new variable in terms of other mathematical entities.
Example: The definition of velocity as v = dx/dt.
The definition of density as mass/volume.
y = f(x)
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6
Elucidation: The class of ‘mathematical’-s that stand for a statement of equality between two mathematical expressions.
Example: 2+3 = 5 x^2 +3x = 5x dv/dt = a sin(x) = y
Comment: An equation with variables can always be represented as:
f(v0, v1, …, vn) = g(v0, v1, …, vn)
where f is the left hand and g the right hand side expressions and v0, v1, …, vn are the variables.
Relations:
IRI: http://emmo.info/emmo/top/math#EMMO_4bc29b0f_8fcc_4026_a291_f9774a66d9b8
Elucidation: A function defined using functional notation.
Example: y = f(x)
Relations:
IRI: http://emmo.info/emmo/middle/math#EMMO_88470739_03d3_4c47_a03e_b30a1288d50c
Elucidation: A mathematica string that can be evaluated as true or false.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_27c5d8c6_8af7_4d63_beb1_ec37cd8b3fa3
Elucidation: An ‘equation’ that stands for a ‘physical_law’ by mathematically defining the relations between physics_quantities.
Comment: The Newton’s equation of motion.
The Schrodinger equation.
The Navier-Stokes equation.
Relations:
IRI: http://emmo.info/emmo/middle/models#EMMO_e5438930_04e7_4d42_ade5_3700d4a52ab7
Elucidation: An ‘equation’ that stands for a physical assumption specific to a material, and provides an expression for a ‘physics_quantity’ (the dependent variable) as function of other variables, physics_quantity or data (independent variables).
Example: The Lennard-Jones potential.
A force field.
An Hamiltonian.
Comment: A material_relation can e.g. return a predefined number, return a database query, be an equation that depends on other physics_quantities.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_4207e895_8b83_4318_996a_72cfb32acd94
Elucidation: A ‘Physical’ that stands for a real world object that represents an amount of a physical substance (or mixture of substances) that constitute (is part of) a more comprehensive real world object.
Comment: The definition states that a ‘Material’ is a portion of a real world object, being that a full functional device or component, or a sample made of that material (or the sample itself).
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_3c218fbe_60c9_4597_8bcf_41eb1773af1f
Elucidation: A ‘Physical’ with no ‘Massive’ parts.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_98ada9d8_f1c8_4f13_99b5_d890f5354152
Elucidation: The perspective for which physical objects are categorized only by concepts coming from physics.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_70dac51e_bddd_48c2_8a98_7d8395e91fc2
Elucidation: A ‘Physical’ with ‘Massless’ parts that are mediators of interactions.
Comment: The concepts of matter and field for classical physics, upon which we can categorize physical entities, are replaced in quantum physics by the more general concepts of quantum field.
Here the class ‘Field’ refers to the quantum field of massless bosonic particles (i.e. photons, gluons), while the class ‘Matter’ refers to the quantum field of massive fermionic or bosonic particles (e.g. quarks, electrons).
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_5b2222df_4da6_442f_8244_96e9e45887d1
Elucidation: A ‘Physical’ that possesses some ‘Massive’ parts.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_8043d3c6_a4c1_4089_ba34_9744e28e5b3d
Elucidation: The class of individuals that stand for electrons elemntary particles.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_7db59e56_f68b_48b7_ae99_891c35ae5c3b
Elucidation: The class of individuals that stand for gluons elementary particles.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_72d53756_7fb1_46ed_980f_83f47efbe105
Elucidation: The class of individuals that stand for quarks elementary particles.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_385b8f6e_43ac_4596_ad76_ac322c68b7ca
Elucidation: The union of classes of elementary particles that possess mass.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_25f8b804_9a0b_4387_a3e7_b35bce5365ee
Comment: The class of individuals that stand for photons elementary particles.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_e5488299_8dab_4ebb_900a_26d2abed8396
Elucidation: The union of classes of elementary particles that do not possess mass.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_eb3c61f0_3983_4346_a0c6_e7f6b90a67a8
Elucidation: The class of individuals that stand for gravitons elementary particles.
Comment: While this particle is only supposed to exist, the EMMO approach to classical and quantum systems represents fields as made of particles.
For this reason graviton is an useful concept to homogenize the approach between different fields.
Relations:
IRI: http://emmo.info/emmo/middle/physicalistic#EMMO_c26a0340_d619_4928_b1a1_1a04e88bb89d
Elucidation: The union of all classes categorizing elementary particles according to the Standard Model.
Comment: Only a subset of elementary particles from the Standard Model are here included for the sake of simplicity.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_3397f270_dfc1_4500_8f6f_4d0d85ac5f71
Elucidation: An atom_based state defined by an exact number of e-bonded atomic species and an electron cloud made of the shared electrons.
Example: H20, C6H12O6, CH4
Comment: An entity is called essential if removing one direct part will lead to a change in entity class.
An entity is called redundand if removing one direct part will not lead to a change in entity class.
Comment: This definition states that this object is a non-periodic set of atoms or a set with a finite periodicity.
Removing an atom from the state will result in another type of atom_based state.
e.g. you cannot remove H from H20 without changing the molecule type (essential). However, you can remove a C from a nanotube (redundant). C60 fullerene is a molecule, since it has a finite periodicity and is made of a well defined number of atoms (essential). A C nanotube is not a molecule, since it has an infinite periodicity (redundant).
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_a2b006f2_bbfd_4dba_bcaa_3fca20cd6be1
Elucidation: A continuum characterized by structural rigidity and resistance to changes of shape or volume, that retains its shape and density when not confined.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_20fff605_465f_4034_8696_e53e90ec83f4
Elucidation: A union of the four base classes for the classification of materials according to the DG-RTD Review of Materials Modelling.
Seealso: https://op.europa.eu/en/publication-detail/-/publication/e0845ae1-1b60-11e7-aeb3-01aa75ed71a1
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_db03061b_db31_4132_a47a_6a634846578b
Elucidation: A standalone atom with an unbalanced number of electrons with respect to its atomic number.
Comment: The ion_atom is the basic part of a pure ionic bonded compound i.e. without eclectron sharing,
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_87ac88ff_8379_4f5a_8c7b_424a8fff1ee8
Elucidation: A continuum that has no fixed shape and yields easily to external pressure.
Example: Gas, liquid, plasma,
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_4588526f_8553_4f4d_aa73_a483e88d599b
Elucidation: A standalone atom that has no net charge.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_8b0923ab_b500_477b_9ce9_8b3a3e4dc4f2
Elucidation: A state that is a collection of sufficiently large number of other parts such that: - it is the bearer of qualities that can exists only by the fact that it is a sum of parts - the smallest partition dV of the state volume in which we are interested in, contains enough parts to be statistically consistent: n [#/m3] x dV [m3] >> 1
Comment: A continuum is made of a sufficient number of parts that it continues to exists as continuum individual even after the loss of one of them i.e. a continuum is a redundant.
Comment: A continuum is not necessarily small (i.e. composed by the minimum amount of sates to fulfill the definition).
A single continuum individual can be the whole fluid in a pipe.
Comment: A continuum is the bearer of properties that are generated by the interactions of parts such as viscosity and thermal or electrical conductivity.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_2fd3f574_5e93_47fe_afca_ed80b0a21ab4
Elucidation: An atom that does not share electrons with other atoms.
Comment: A standalone atom can be bonded with other atoms by intermolecular forces (i.e. dipole–dipole, London dispersion force, hydrogen bonding), since this bonds does not involve electron sharing.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_8303a247_f9d9_4616_bdcd_f5cbd7b298e3
Elucidation: An bonded atom that shares at least one electron to the atom-based entity of which is part of.
Comment: A real bond between atoms is always something hybrid between covalent, metallic and ionic.
In general, metallic and ionic bonds have atoms sharing electrons.
Comment: The bond types that are covered by this definition are the strong electonic bonds: covalent, metallic and ionic.
Comment: This class can be used to represent molecules as simplified quantum systems, in which outer molecule shared electrons are un-entangled with the inner shells of the atoms composing the molecule.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_eb77076b_a104_42ac_a065_798b2d2809ad
Elucidation: A standalone atom has direct part one ‘nucleus’ and one ‘electron_cloud’.
An O ‘atom’ within an O2 ‘molecule’ is an ‘e-bonded_atom’.
In this material branch, H atom is a particular case, with respect to higher atomic number atoms, since as soon as it shares its electron it has no nucleus entangled electron cloud.
We cannot say that H2 molecule has direct part two H atoms, but has direct part two H nucleus.
Comment: An ‘atom’ is a ‘nucleus’ surrounded by an ‘electron_cloud’, i.e. a quantum system made of one or more bounded electrons.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_1067b97a_84f8_4d22_8ace_b842b8ce355c
Elucidation: A ‘spacetime’ that stands for a quantum system made of electrons.
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_8f87e700_99a8_4427_8ffb_e493de05c217
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_f835f4d4_c665_403d_ab25_dca5cc74be52
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_7d66bde4_b68d_41cc_b5fc_6fd98c5e2ff0
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_50781fd9_a9e4_46ad_b7be_4500371d188d
Relations:
IRI: http://emmo.info/emmo/middle/materials#EMMO_df808271_df91_4f27_ba59_fa423c51896c
Relations:
IRI: http://emmo.info/emmo/top/mereotopology#EMMO_08cb807c_e626_447b_863f_e2835540e918
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_361c25b3_3c0d_4066_b622_72dcc71ab5cf
Relations:
IRI: http://emmo.info/emmo/middle/siunits#EMMO_05083b9c_c9d1_4202_b22d_5249067772ac
Relations:
