Contacts:
Gerhard Goldbeck
Goldbeck Consulting Ltd (UK)
email: gerhard@goldbeck-consulting.com
Emanuele Ghedini
University of Bologna (IT)
email: emanuele.ghedini@unibo.it
European Materials and Modelling Ontology (EMMO)
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.
It provides the connection between the physical world, materials characterisation world and materials modelling world.
The European Materials Modelling Ontology
Development Version v0.9.9
The European Materials Modelling Ontology
Version 0.9.9
EMMO is released under a Creative Commons license Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/by/4.0/legalcode
definition
elucidation
example
mereotopology
has_spatial_proper_part
Actually, the connection relation upon which is based the enclosure relation is considered as primitive, i.e. undefined and only declared by the user.
For practical purpose however, the EMMO bases the relations on enclosure level, giving the lower relations for granted, and considering enclosure as primitive, even if it's derived by lower level axioms.
Definition:
Cxy := x is connected with y
Axiom:
1) Cxx (x is always connected with itself (reflexivity))
Axiom:
2) Cxy->Cyx (if x is connected with y than y is connected with x (symmetry))
Definition:
Exy <=> (Czx->Czy) Definition: x is enclosed in y
Theorem: E is reflexive, transitive and antisymmetric.
Axiom:
3) (Exa<=>Exb) <=> a=b (extensionality axiom)
Axiom (see 'is_part_of' relation for definition of Pxy):
4) Pxy->Exy (if x is part of y then y encloses x (monotonicity))
Axioms 1) 2) 3) defines the Ground Topology (T).
Axioms 1) 2) 3) 4) defines the MereoTopology (MT).
is_enclosed_by
is_space_slice_of
has_part
has_time_slice
has_projection
has_subdimension
is_projection_of
has_spatial_part
has_space_slice
contacts
disconnected
is_temporal_proper_part_of
set_theory
connected
intersect
has_member
Definition:
PPxy := Pxy && not(x=y)
is_proper_part_of
has_temporal_part
is_spatial_proper_part_of
Dimensionality between domain and range cannot change.
P is the is_part_of relation.
Axioms:
1) Pxx (reflexivity)
2) (Pxy && Pyz) -> Pxz (transitivity)
3) (Pxy && Pyz) -> x=y (antisymmetry)
4) not(Pyx) -> exists z (Pzy and not Ozx) (strong supplementation)
with:
Ozx := exists z (Pzx and Pzy) (overlap)
(Extensional Mereology)
Since EMMO is based on MereoTopology (MT), the axiom Pxy->Exy (x is part of y implies x is enclosed by y) implies that 'is_part_of' is a subproperty of 'is_enclosed_by'.
is_part_of
encloses
has_temporal_proper_part
has_proper_part
overcrosses
Dimensionality between domain and range must change.
is_subdimension_of
is_spatial_part_of
A partitioning that extends along the whole temporal dimension of an hybrid.
is_temporal_part_of
A partitioning that extends along the whole spatial dimension of a substrate.
is_time_slice_of
overlaps
The primitive relation that assigns an 'item' to a 'set'.
is_member_of
relation
is_spatial_direct_part_of
DSPxy :=
y can be partitioned in a set of x_i spatial proper parts that:
- for all i,j x_i and x_j do not overlap
- the union of x_i covers the whole D
- there exists no k spatial proper part of y for which SPPxk
- x is spatial direct part of only y
is_temporal_direct_part_of
DTPxy :=
y can be partitioned in a set of x_i temporal proper parts that:
- for all i,j x_i and x_j do not overlap
- the union of x_i covers the whole D
- there exists no k temporal proper part of y for which TPPxk
- x is temporal direct part of only y
has_temporal_direct_part
has_spatial_direct_part
has_value
is_value_for
is_model_for
has_model
is_participant_of
has_participant
has_proper_participant
is_proper_participant
is_property_for
has_property
semiotic
is_convention_for
has_index
has_icon
has_sign
stands_for
is_index_of
is_icon_of
has_convention
'elementary' is by definition the most simple example of 'state'.
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.
elementary
The basic constituent of 'physical'-s that can be proper partitioned only in time.
line
1D space entity
A 1D (space) + 0D (time) substrate.
space
Pure space dimensional entities.
void
A 'spacetime' that has no 'elementary' parts.
'set' class can be used to declare individuals that stand for collections of things that do not form a whole in mereotopological sense.
e.g. the set of users of a particular software, the set of atoms that have been part of that just dissociated molecule, or even the set of atoms that are part of a molecule considered as single individual entities and not a mereological fusion.
A 'set' individual cannot be member of a 'set' (to avoid Russel's paradox).
Since OWL classes are intended as sets, we can consider the 'set' branch as a meta-ontological branch, since 'item' class and all its subclasses are then individuals of 'set'.
It is also possible to define a relation 'is_subset_of' valid only between 'set' individuals that is equivalent to the OWL-DL built-in 'is_a' relation between classes in the 'item' branch.
However this is not done in the EMMO for the sake of simplicity.
set
The class of individuals that 'has_member' some 'item' (i.e. that stand for a collection of 'item' individuals).
The class representing the collection of all the individuals (signs) that represents a collection of 'item' individuals.
true
world_sheet
1D space entity unfolding in time
A 1D (space) + 1D (time) substrate.
surface
2D space entity
A 2D (space) + 0D (time) substrate.
point
0D space entity
A 0D (space) + 0D (time) substrate.
volume
3D space entity
A 3D (space) + 0D (time) substrate.
hybrid
Entities that unfolds in space and time.
'emmo' is the disjoint union of 'item' and 'set' (covering axiom).
Union implies that real things that are represented by 'emmo' individuals can only be 'item' individuals (for which mereology applies) or 'set' individuals (for which set theory applies).
Disjointness means that a 'set' individual cannot be an 'item' individual and viceversa, following the fact that e.g. the 'set' individual that stand for some human beings is not a human being itself.
A 'set' individual is a collection of other individuals through the membership relation (e.g. the 'set' individual that stands for all red objects), while an 'item' individual stands for a whole made of parts (e.g. a car made of components).
emmo
The class representing the collection of all the individuals declared in this ontology.
world_volume
2D space entity unfolding in time
A 2D (space) + 1D (time) substrate.
interval
1D time entity
A 0D (space) + 1D (time) substrate.
time
Pure time dimensional entities.
A 'physical' is the class that contains all the individuals that stands real world perceivable entities.
Real world entities must be perceived by the ontologist declaring the corresponding individual.
A 'physical' must include at least an 'elementary' part, but can also 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:
a) 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.)
b) take into account the fact that large entities (e.g. devices, cars, materials) have some void into them.
e.g. a 'spacetime' that has spatial parts an atom and a cubic light year of 'void' extending for some time can be a 'physical' individual.
A 'physical' with dimensions other than 3D+1D (i.e. 'physical' and not 'spacetime') cannot exist, since perception is a process (unfolds in time).
For this reason, 'physical'-s exist only in space and time (3D + 1D), so 'physical' is a subclass of 'spacetime'.
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.
In the EMMO there are no relations such as 'occupies_space', since 'physical'-s are themselves 'spacetime' entities.
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.
1) De Broglie - Bohm interpretation
The most simple approach is to rely on Bohmian mechanics, in which each particle is supposed to exists in a specific position between measurements (hidden variables approach), while its trajectory is calculated using a Guiding Equation based on a quantum field calculated with the Schroedinger Equation.
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).
2) Copenhagen interpretation
In this interpretation the properties (e.g. energy level, position, spin) of a particle are not defined in the interval between two measurements and the quantum system is entangled (i.e. properties of particles in the sysyem are correlated) and described by a global wavefunction obtained solving the Schroedinger Equation.
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:
a) 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.
b) 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)
c) 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!
d) 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'.
The purpose of the 'physical' branch is to provide a representation of the real world entities, while the models used to explain or predict the behaviour of the entities lay under the 'semeion' branch.
More than one model can be connected to the same 'physical'.
e.g. Navier-Stokes or Euler equation applied to the same fluid
physical
A 'spacetime' that is an 'elementary' or has some 'elementary' as proper parts and whose temporal proper parts are only 'physical'-s (i.e. it can be perceived without interruptions in time).
A 'spacetime' can be a 'physical' (perceivable) or a 'void' (pure geometrical entity that originates no perception).
'spacetime' is then the superclass for every real world entity which are represented as 3D (space) +1D (time) entities.
The EMMO basic assumption is that the real world (the world outside us) manifests itself as a one spacetime entity, the Universe.
Some mereological parts (regions) of the Universe express peculiar properties that can be perceived by (they interact with) an interpreter/ontologist.
These mereological parts can be categorized in matter spacetimes or field spacetimes individuals.
'physical' class is the union of 'field' and 'matter' classes.
spacetime
3D space entity unfolding in time
A 3D (space) + 1D (time) substrate.
A 'spacetime' entity can directly or indirectly interact with the ontologist (can be perceived) or can be simply a void region of spacetime (originates no perceptions).
The former type of 'spacetime' is called 'physical' and the latter 'void'.
The use of a disjoint union axiom is self-evident.
The concept of perception is considered as primitive.
'item' is a disjoint union of three subclasses (covering axiom).
The union categorizes 'item'-s in:
- pure space individuals (3D)
- pure time individuals (1D)
- hybrid individuals, which are categorized in
- world lines (0D+1D)
- world sheets (1D+1D)
- world volume (2D+1D)
- spacetime (3D+1D).
Disjointness means that 'item'-s cannot have multiple-dimensional representations.
An 'item' is a fundamental mereotopological (MT) entity, so that the primitive property of enclosure can be defined for it.
MT relations occurs only between 'item' individuals. 'item' is the highest superclass for all wholes and parts.
'item'-s are always topologically connected spaces (a topological space X is said to be disconnected if it is the union of two disjoint nonempty open sets. Otherwise, X is said to be connected).
In the EMMO the 'item' individuals exists in a 4D substrate. 'item' individuals span through time (1D) and space (3D) dimensions and sub-dimensions.
Parthood relations does not change dimensionality of an 'item' individual (e.g. a 4D individual has only 4D parts, a spacetime has
no space parts).
Changes in dimensionality come from pure topological relations between subspaces (i.e. slicing).
The 'item' class and all its sub-classes are 'set' individuals.
The 'item' branch will be used to represent the world things and can be seen in practice as the ontology core.
item
Superclass for all individuals that are subjected to MT MereoTopology.
The class that collects all the individuals that are member of a set (it’s the most comprehensive set individual).
instant
0D time entity
A 0D (space) + 0D (time) substrate.
world_line
0D space entity unfolding in time
A 0D (space) + 1D (time) substrate.
Direct partitions declaration is a choice of the ontology developer 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.
The definition of 'state' implies that its 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 granularity of 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 within a 'state'.
Also, the 'state' must cover all the time interval between two successive cardinality changes.
The use of spatial direct parthood in 'state' definition means that a 'state' cannot overlap in space another 'state'.
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'.
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.
state
A 'physical' whose spatial direct parts extends from one change in spatial direct part cardinality (i.e. the number of spatial direct parts) to the immidiate next change.
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.
'existent' is the most important class to be used for representing real world changing things.
This class is used to represent the whole life of a complex state-changing physical entity that for the all the extent of its life has a meaning for the ontologist.
e.g. a car, a supersaturated gas with nucleating nanoparticles, an atom that becomes ionized and then recombines with an electron.
A 'physical' and not 'existent' individual is something not classifiable because no common terms or definitions have been developed to name it. Such type of individual can be declared but it has no class (at least not yet) in the taxonomy.
i.e. an heterogeneous heap of elementaries, appearing and disappering in time.
A superclass that contains in a taxonomy all physicals that can be classifed in some way by the ontologist.
ex-sistere (latin): to stay (to persist through time) outside others of the same type (to be distinct from the rest).
existent
A 'physical' which is a 'state' or made only of 'state' temporal direct parts.
electron_cloud
A 'spacetime' that stands for a quantum system made of electrons.
mesoscopic
photon
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.
standalone_atom
An atom that does not share electrons with other atoms.
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.
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).
molecule
An atom_based state defined by an exact number of e-bonded atomic species and an electron cloud made of the shared electrons.
H20, C6H12O6, CH4
2
1
massive
vacuum
neutral_atom
A standalone atom that has no net charge.
nucleon
matter
atomic
quark
subatomic
gluon
electron
A real bond between atoms is always something hybrid between covalent, metallic and ionic.
In general, metallic and ionic bonds have atoms sharing electrons.
The bond types that are covered by this definition are the strong electonic bonds: covalent, metallic and ionic.
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.
e-bonded_atom
An electronic bonded atom that shares at least one electron to the atom_based entity of which is part of.
fluid
A continuum that has no fixed shape and yields easily to external pressure.
Gas, liquid, plasma,
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.
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.
A continuum is the bearer of properties that are generated by the interactions of parts such as viscosity and thermal or electrical conductivity.
continuum
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
proton
solid
A continuum characterized by structural rigidity and resistance to changes of shape or volume, that retains its shape and density when not confined.
The ion_atom is the basic part of a pure ionic bonded compound i.e. without eclectron sharing,
ion_atom
A standalone atom with an unbalanced number of electrons with respect to its atomic number.
neutron
massless
graviton
atom
An 'atom' is a 'nucleus' surrounded by an 'electron_cloud', i.e. a quantum system made of one or more bounded electrons.
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.
1
1
nucleus
1
math_symbol
A 'symbol' that is part of standard mathematical formalism.
number
A 'variable' is a 'symbol' that stands for a numerical defined 'mathematical' entity like e.g. a number, a vector, a matrix.
variable
The class of general mathematical symbols.
mathematical
pi = 3.14
constant
A 'varaible' that stand for a well known constant.
A 'variable' whose value is assumed to be known independently from the equation, but whose value is not explicitated in the equation.
parameter
Viscosity, the total energy of the system given by an Hamiltonian, the force between two atoms.
The class of 'mathematical'-s that stand for a mathematical expression that puts in relation some variables and that 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.
e.g.
x^2 +3x = 5x
dv/dt = a
sin(x) = y
equation
unknown
The dependent variable for which an equation has been written.
Velocity, for the Navier-Stokes equation.
The Newton's equation of motion.
The Schrodinger equation.
The Navier-Stokes equation.
physics_equation
An 'equation' that stands for a 'physical_law' by mathematically defining the relations between physics_quantities.
physical_phenomenon
continuum_model
mesoscopic_model
theorization
The 'semiosis' process of interpreting a 'physical' and provide a complec sign, 'theory' that stands for it and explain it to another interpreter.
electronic_model
atomistic_model
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
theory
A 'conventional' that stand for a 'physical'.
A 'model' prediction is always a prediction of the properties of an entity, since an entity is known by an interpreter only through perception.
model
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).
physical_law
data_based_model
A computational model that uses data to create new insight into the behaviour of a system.
physics_based_model
A solvable set of one Physics Equation and one or more Materials Relations.
natural_law
A material_relation can e.g. return a predefined number, return a database query, be an equation that depends on other physics_quantities.
material_relation
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).
The Lennard-Jones potential.
A force field.
An Hamiltonian.
material_law
mathematical_model
process
A 'process' is defined as a temporal part of a 'physical' that is categorized in a primitive process subclass according to what type of process we want to represent.
Strictly speaking, every 'physical' is a process since in a 4D representation it always has a time dimension, but in the EMMO we restrict the meaning of ‘process’ to 'physical'-s whose evolution in time have a particular meaning for the ontologist.
i.e. a 'process' is not only something that unfolds in time (which is automatically represented in a 4D ontology), but something happening that has a meaning for the interpreter.
A 'process' is always a 'physical', since a 'void' does not have elements that evolves in time.
However, 'void' parts inside a 'process' can be a 'participant'.
A temporal part of a 'physical' that identifies a particular type of evolution in time.
participant
A portion of a 'process' that participates to the 'process' with a specific role.
In the EMMO the relation of participation to a process falls under mereology.
It can be a 'physical' or a 'void'.
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.
physical_quantity
A "symbolic" entity that is made of a 'number' and a 'measurement_unit'.
By definition it also stands for the result of a measurement process, and so it is also a 'sign'.
observation
A 'semiosis' that involves an 'observer' 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.
observer
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.
A 'subjective_property' cannot be used to univocally compare 'object'-s.
e.g. you cannot evaluate the beauty of a person on objective basis.
subjective_property
A 'property' that cannot be univocally determined and is strongly 'observer' dependent.
The beauty of that girl.
The style of your clothing.
physical_property
A 'property' that is determined by each 'observer' following a well defined 'observation' procedure through a specific perception channel.
measurement
An 'observation' that results in a quantitative comparison of a 'property' of an 'object' with a standard reference.
qualitative_property
An 'physical_property' that cannot be quantified.
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
measurement_unit
A 'quantitative_property' that stands for the standard reference magnitude of a specific class of measurement processes, defined and adopted by convention or by law.
Quantitative measurement results are expressed as a multiple of the 'measurement_unit'.
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).
property
A 'sign' that stands for an 'object' that the 'interpreter' perceived through a well defined 'observation' process.
(a property is always a partial representation of an 'object' since it reflects the 'object' capability to be part of a specific 'observation' process)
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.
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.
descriptive_property
quantitative_property
A 'property' 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.
measurement_instrument
semiosis
A 'process', that has participant an 'interpreter', that is aimed to produce a 'sign' representing another participant, the 'interpreted'.
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
interpreter
The entity (or agent, or observer, or cognitive entity) who connects 'sign', 'interpretant' and 'object'.
interpretant
In formal languages it is called a string of symbols.
symbolic
A 'symbol' or a composition of 'symbol'-s.
fe@è0
emmo
!5*a
cat
index
A 'sign' that stands for an 'objectì due to causal continguity.
Smoke stands for a combustion process (a fire).
My facial expression stands for my emotional status.
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.
conventional
A 'sign' that stand for an 'object' through convention, norm or habit, without any resemblance to it.
well-formed
A composition of 'symbol'-s respecting a specific language syntactic rules (well-formed).
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.
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).
object
The object, in Peirce semiotics.
Subclasses of 'symbol' are alphabets, in formal languages terminology.
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)
The class is the idea of the symbol, while the individual of that class stands for a specific mark (or token) of that idea.
symbol
An elementary mark of a specific symbolic code (alphabet).
The class of letter "A" is the symbol as idea and the letter A is the mark.
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.
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
In a 4D ontology one could question if a 'sign' should be defined as a spatial direct part of a 'semiosis' i.e. a proper part of a 'semiosis' during all its existence.
e.g. one can say that an unread text is not a 'sign': it was a 'sign' during the 'semiosis' process in which it was written, but after that it is something else, until somebody read it again.
However, this is not the case for an ontology, since declaring an individual under the 'sign' class (a semiosis outside the EMMO, a meta-semiosis) is equivalent to say that for the ontologist (an interpreter outside the EMMO, a meta-interpreter) the real entity (an object outside the EMMO, a meta-object) is a 'sign'.
So the 'semiosis' process within the EMMO is about how other 'interpreter'-s deal with the 'sign'-s here declared.
It can be defined as the semiotic branch of the EMMO.
'sign' subclasses categorize the type of signs that are used to create representations/models of the real world entities.
sign
An 'spacetime' that is used as sign ("semeion" in greek) that stands for another 'spacetime' through an semiotic process.
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.
semiotic
The class of semiotic elements used in 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'
Three subtypes of icon are possible:
(a) the image, which depends on a simple quality (e.g. picture)
(b) the diagram, whose internal relations, mainly dyadic or so taken, represent by analogy the relations in something (e.g. math formula, geometric flowchart)
(c) the metaphor, which represents the representative character of a sign by representing a parallelism in something else
[Wikipedia]
icon
A 'sign' that stands for an 'object' by resembling or imitating it, in shape or by sharing a similar logical structure.
A picture that reproduces the aspect of a person.
An equation that reproduces the logical connection of the properties of a physical entity.
material
component
While the 'state' branch describes single simple entities (e.g. atoms, molecules, nanoparticles), the 'engineered_entity' branch describe entities that show some level of complexity/heterogeneity in their composition, and are made for a specific use.
Classes in this branch are primitive.
e.g. car, tire, composite material.
engineered_entity
An 'existent' that is a parthood composition of 'state' individuals for a particular purpose.
system
license
“Granularity” stands for “matter with a particular granularity” .
Granularity is then defined as a superclass of defined subclasses that are defined as matter that is composed of specific types of objects
(and vacuum) and whose partitions respect direct parthood criteria.
The granularity class (and its inherited classes) is useful since a reasoner can automatically puts the individuals defined by the user under a generic class that expresses clearly the types of its compositional parts.
Since most of physics based modelling tools are designed to describe systems made of a specific base-object (e.g. atoms, fluids, particles) the granularity classes can be directly linked to model types.
A 'process' individual is easily defined as a temporal part of a physical that is categorized in a primitive process subclass according to what type of process we want to represent.
Strictly speaking, every physical is a ‘process’ since it always has a time dimension, but here we restrict the meaning of ‘process’ to physicals whose evolution in time have a meaning for the material ontologist.
Participants of a process are always parts of that particular process (i.e. they are spacetime). It means that is_participant relation is subclass of is_part_of relation (e.g. you cannot participate to a party if you are not enclosed by the party room)
Matter is always 4D! There is no 3D representation of matter.
There can be a 3D slice of a matter but is no more matter: it’s simply a 3D spatial region.
A model can be an abstraction for simple entities (e.g. an atom, a field) or a more complex existent.
A model is an abstraction for a physical entity.
A 'substrate' individual represents a place (in general sense) in which real world item exists.
A 'substrate' individual provides the dimensions of existence for real world entities. It follows the fact that everything that exists is placed
somewhere and space and time coordinates can be used to identify
it.
This restriction in the mereological relations is done in order to overcome a typical misuse of the partitioning procedure, that occurs when the user wants to stretch the is_part_of relation beyond its applicability limit.
e.g. you can slice a 3D+1D cake in 3D+1D thin parts (3 spatial + 1 temporal dimension), but it’s impossible to slice the cake in infinitely thin 2D+1D slices (2 spatial + 1 temporal dimension). The relation of parthood applied to material entities cannot reduce spatial dimensions for a material object, since a 2D+1D material object does not exist!
Slicing a 3D+1D entity in a 2D+1D entity can still be done, but within the substrate level (the topological level) using
the is_slice_of relation working on geometrical concepts and not actual materials.
Substrate is the disjoint union of spacetime (4D), space (3D), surface (2D) and time (1D).
A 'mathematical' that has no variables.
In the following classes annotations we will often shorten expressions like:
- an individual of class 'my_class'
- individuals of class 'my_class'
with the expressions:
- a 'my_class'
- some 'my_class'-es