A unique string describing the physical dimensionality of a physical quantity.
See the comments of PhysicalDimension for a description of this "regex" string.
physicalDimension
URL to corresponing entity in QUDT.
http://www.qudt.org/2.1/catalog/qudtcatalog.html
qudtEntry
Replaced by skos:altLabel
altLabel
URL to corresponding entry in the IEC Electropedia online database of ISO 80000 terms and definitions of quantities and units available at http://www.electropedia.org/.
http://www.electropedia.org/
IECEntry
Replaced by dcterms:license
license
URL to corresponding concept in DBpedia.
https://wiki.dbpedia.org/
dbpediaEntry
Human readable definition of a concept.
definition
3‑1.1 (refers to length)
Corresponding item number in ISO 80 000.
https://www.iso.org/obp/ui/#iso:std:iso:80000:1:ed1:v1:en
ISO80000Ref
Short enlightening explanation of a concept.
elucidation
URL to CODATA Internationally recommended 2018 values of physical constants.
https://physics.nist.gov/cuu/Constants/index.html
codataEntry
URL to corresponding concept in the Basic Datatype Ontology (DBO)
https://github.com/TechnicalBuildingSystems/Ontologies/blob/master/BasicDataTypeOntology/ontology.ttl
bdoMatch
Illustrative example of how the entity is used.
example
URL to corresponding Wikipedia entry.
https://www.wikipedia.org/
wikipediaEntry
Replaced by dcterms:creator
author
IRI to corresponding concept in the Ontology of units of Measure
https://enterpriseintegrationlab.github.io/icity/OM/doc/indexen.html
https://github.com/HajoRijgersberg/OM
omMatch
DOI to corresponding concept in IUPAC
https://goldbook.iupac.org/
iupacEntry
EMMO applies the naming convension to its subproperties of rdfs:seeAlso that their label must end with one of the following terms:
 'Match': resolvable URLs to corresponding entity in another ontology
 'Entry': resolvable URLs to a human readable resource describing the subject
 'Ref': nonresolvable reference to a human readable resource describing the subject
Indicate a resource that might provide additional information about the subject resource.
The relation between a process and an object participating to it.
Participation is a parthood relation: you must be part (and then be connected) of the process to contribute to it.
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.
hasParticipant
hasProperParticipant
hasVariable
Relates the physical quantity to its unit through spatial direct parthood.
In EMMO version 1.0.0beta, physical quantities used the hasReferenceUnit object property to relate them to their units via physical dimensionality. This was simplified in 1.0.0alpha3 in order to make reasoning faster.
The restriction (e.g. for the physical quantity Length)
Length hasReferenceUnit only (hasPhysicsDimension only LengthDimension)
was in 1.0.0alpha3 changed to
Length hasPhysicsDimension some LengthDimension
Likewise were the universal restrictions on the corresponding unit changed to excistential. E.g.
Metre hasPhysicsDimension only LengthDimension
was changed to
Metre hasPhysicsDimension some LengthDimension
The label of this class was also changed from PhysicsDimension to PhysicalDimension.
hasReferenceUnit
Relates a quantity to its reference unit through spatial direct parthood.
hasQuantityValue
hasPhysicalDimension
hasModel
hasProperty
hasTemporalDirectPart
hasSpatioTemporalDirectPart
hasSpatialDirectPart
The generic EMMO semiotical relation.
semiotical
hasIndex
hasIcon
hasSign
hasInterpretant
hasConvention
The superclass for all EMMO mereotopological relations.
Mereotopology merges mereological and topological concepts and provides relations between wholes, parts, boundaries, etc.
mereotopological
hasPart
hasContactWith
disconnected
Causality is a topological property between connected items.
Items being connected means that there is a topological contact or "interaction" between them.
connected
hasMember
Enclosure is reflexive and transitive.
encloses
hasProperPart
overcrosses
hasOverlapWith
The superclass for all relations used by the EMMO.
EMMORelation
A relation that isolates a proper part that extends itself in time through a portion of the lifetime whole.
hasSpatioTemporalPart
A relation that isolate a proper part that covers the total spatial extension of a whole within a time interval.
hasTemporalPart
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).
hasSpatialPart
hasNumericalData
hasSymbolData
A union of classes that categorize physicals under a holistic perspective: the interest is on the whole 4D object (process) and the role of its 4D parts (participants) without going further into specifying the spatial hierarchy or the temporal position of each part.
An holistic perspective considers each part of the whole as equally important, without the need of a granularity hierarchy (in time or space).
A molecule of a body can have role in the body evolution, without caring if its part of a specific organ and without specifying the time interval in which this role occurred.
This class allows the picking of parts without necessarily going trough a rigid hierarchy of spatial compositions (e.g. body > organ > cell > molecule) or temporal composition.
Holism (from Greek ὅλος holos "all, whole, entire")
Holistic
A temporal part of a physical that identifies a particular type of evolution in time.
A 'Process' is always a 'Physical', since a 'Void' does not have elements that evolves in time.
Following the common definition of process, the reader may think that 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 (i.e. every 4D object unfolds in time, but not every 4D object may be of interest 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).
Process
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 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.
Participant
T+1 L0 M0 I0 Θ0 N0 J0
TimeDimension
T1 L+1 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Velocity
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130132
Vector quantity giving the rate of change of a position vector.
 ISO 800003
3‑10.1
The velocity depends on the choice of the reference frame. Proper transformation between frames must be used: Galilean for nonrelativistic description, Lorentzian for relativistic description.
 IEC, note 2
The velocity is related to a point described by its position vector. The point may localize a particle, or be attached to any other object such as a body or a wave.
 IEC, note 1
Velocity
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MoleFraction
http://dbpedia.org/page/Mole_fraction
The amount of a constituent divided by the total amount of all constituents in a mixture.
http://www.ontologyofunitsofmeasure.org/resource/om2/AmountOfSubstanceFraction
https://doi.org/10.1351/goldbook.A00296
MoleFraction
AmountFraction
T2 L+2 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Inductance
http://dbpedia.org/page/Inductance
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.
https://doi.org/10.1351/goldbook.M04076
Inductance
ElectricInductance
T2 L+1 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Weight
http://dbpedia.org/page/Weight
https://doi.org/10.1351/goldbook.W06668
Force of gravity acting on a body.
Weight
T0 L3 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Density
http://dbpedia.org/page/Density
https://doi.org/10.1351/goldbook.D01590
Mass per volume.
Density
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/AtomicNumber
http://dbpedia.org/page/Atomic_number
Number of protons in an atomic nucleus.
https://doi.org/10.1351/goldbook.A00499
AtomicNumber
T2 L+1 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/ElectromagneticPermeability
http://dbpedia.org/page/Permeability_(electromagnetism)
https://doi.org/10.1351/goldbook.P04503
Measure for how the magnetization of material is affected by the application of an external magnetic field .
ElectromagneticPermeability
Permeability
T3 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Power
http://dbpedia.org/page/Power_(physics)
Rate of transfer of energy per unit time.
https://doi.org/10.1351/goldbook.P04792
Power
T0 L0 M0 I0 Θ0 N0 J0
Probability is a dimensionless quantity that can attain values between 0 and 1; zero denotes the impossible event and 1 denotes a certain event.
https://doi.org/10.1351/goldbook.P04855
The propability for a certain outcome, is the ratio between the number of events leading to the given outcome and the total number of events.
Probability
T+4 L3 M1 I+2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Permittivity
http://dbpedia.org/page/Permittivity
http://www.ontologyofunitsofmeasure.org/resource/om2/Permittivity
https://doi.org/10.1351/goldbook.P04507
Measure for how the polarization of a material is affected by the application of an external electric field.
Permittivity
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Heat
https://doi.org/10.1351/goldbook.H02752
Heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter.
Heat
T0 L0 M0 I0 Θ0 N0 J+1
LuminousIntensityDimension
T+1 L0 M0 I+1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/ElectricCharge
http://dbpedia.org/page/Electric_charge
The physical property of matter that causes it to experience a force when placed in an electromagnetic field.
https://doi.org/10.1351/goldbook.E01923
Charge
ElectricCharge
T0 L3 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MassConcentration
http://dbpedia.org/page/Mass_concentration_(chemistry)
https://doi.org/10.1351/goldbook.M03713
Mass of a constituent divided by the volume of the mixture.
MassConcentration
T0 L0 M0 I0 Θ0 N1 J0
http://qudt.org/vocab/constant/AvogadroConstant
The number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole.
It defines the base unit mole in the SI system.
https://physics.nist.gov/cgibin/cuu/Value?na
https://doi.org/10.1351/goldbook.A00543
The DBpedia definition (http://dbpedia.org/page/Avogadro_constant) is outdated as May 20, 2019. It is now an exact quantity.
AvogadroConstant
T+1 L+1 M0 I+1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/ElectricDipoleMoment
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1211135
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1211136
http://dbpedia.org/page/Electric_dipole_moment
An electric dipole, vector quantity of magnitude equal to the product of the positive charge and the distance between the charges and directed from the negative charge to the positive charge.
http://www.ontologyofunitsofmeasure.org/resource/om2/ElectricDipoleMoment
https://doi.org/10.1351/goldbook.E01929
ElectricDipoleMoment
Base quantities defined in the International System of Quantities (ISQ).
https://en.wikipedia.org/wiki/International_System_of_Quantities
ISQBaseQuantity
T+1 L+1 M0 I+1 Θ0 N0 J0
MagneticDipoleMomentDimension
T0 L1 M0 I0 Θ0 N0 J0
http://dbpedia.org/page/Vergence
In geometrical optics, vergence describes the curvature of optical wavefronts.
Vergence
T2 L+1 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Force
http://dbpedia.org/page/Force
Any interaction that, when unopposed, will change the motion of an object.
https://doi.org/10.1351/goldbook.F02480
Force
T0 L0 M+1 I0 Θ0 N0 J0
The mass of an atom in the ground state.
https://en.wikipedia.org/wiki/Atomic_mass
https://doi.org/10.1351/goldbook.A00496
Since the nucleus account for nearly all of the total mass of atoms (with the electrons and nuclear binding energy making minor contributions), the atomic mass measured in Da has nearly the same value as the mass number.
The atomic mass is often expressed as an average of the commonly found isotopes.
AtomicMass
Derived quantities defined in the International System of Quantities (ISQ).
ISQDerivedQuantity
T3 L+2 M+1 I1 Θ0 N0 J0
ElectricPotentialDimension
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Energy
http://dbpedia.org/page/Energy
A property of objects which can be transferred to other objects or converted into different forms.
https://doi.org/10.1351/goldbook.E02101
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.
Energy
T+3 L2 M1 I+2 Θ0 N0 J0
ElectricConductanceDimension
T0 L2 M0 I0 Θ0 N0 J0
AreaDimension
T2 L+2 M+1 I1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MagneticFlux
http://dbpedia.org/page/Magnetic_flux
Measure of magnetism, taking account of the strength and the extent of a magnetic field.
https://doi.org/10.1351/goldbook.M03684
MagneticFlux
T2 L+2 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/DoseEquivalent
http://dbpedia.org/page/Energy
A dose quantity used in the International Commission on Radiological Protection (ICRP) system of radiological protection.
https://doi.org/10.1351/goldbook.E02101
DoseEquivalent
T2 L+2 M+1 I0 Θ1 N0 J0
EntropyDimension
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Enthalpy
http://dbpedia.org/page/Enthalpy
https://doi.org/10.1351/goldbook.E02141
Measurement of energy in a thermodynamic system.
Enthalpy
T1 L+1 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Momentum
http://dbpedia.org/page/Momentum
https://doi.org/10.1351/goldbook.M04007
Product of mass and velocity.
Momentum
T0 L+1 M0 I0 Θ0 N0 J0
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130312
Vector r characterizing a point P in a point space with a given origin point O.
In the usual geometrical threedimensional space, position vectors are quantities of the dimension length.
 IEC
Position vectors are socalled bounded vectors, i.e. their magnitude and direction depend on the particular coordinate system used.
 ISO 800003
Position
PositionVector
T0 L0 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/constant/ElectronMass
http://dbpedia.org/page/Electron_rest_mass
https://physics.nist.gov/cgibin/cuu/Value?me
https://doi.org/10.1351/goldbook.E02008
The rest mass of an electron.
ElectronMass
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/PotentialEnergy
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130348
http://dbpedia.org/page/Potential_energy
The energy possessed by a body by virtue of its position or orientation in a potential field.
http://www.ontologyofunitsofmeasure.org/resource/om2/PotentialEnergy
https://doi.org/10.1351/goldbook.P04778
PotentialEnergy
T2 L+2 M+1 I1 Θ0 N0 J0
MagneticFluxDimension
T3 L+2 M+1 I1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Voltage
http://dbpedia.org/page/Voltage
Energy required to move a unit charge through an electric field from a reference point.
https://doi.org/10.1351/goldbook.A00424
Voltage
ElectricPotential
T1 L+1 M0 I0 Θ0 N0 J0
SpeedDimension
T1 L+2 M+1 I0 Θ0 N0 J0
AngularMomentumDimension
T+3 L1 M1 I0 Θ0 N0 J+1
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.
https://physics.nist.gov/cgibin/cuu/Value?kcd
Defines the Candela base unit in the SI system.
LuminousEfficacyOf540THzRadiation
T2 L1 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Pressure
http://dbpedia.org/page/Pressure
The force applied perpendicular to the surface of an object per unit area over which that force is distributed.
https://doi.org/10.1351/goldbook.P04819
Pressure
T0 L0 M0 I0 Θ0 N0 J+1
http://qudt.org/vocab/quantitykind/Length
http://dbpedia.org/page/Luminous_intensity
A measure of the wavelengthweighted 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.
LuminousIntensity
T1 L0 M0 I0 Θ0 N0 J0
FrequencyDimension
T2 L1 M+1 I0 Θ0 N0 J0
PressureDimension
T2 L+1 M+1 I0 Θ0 N0 J0
ForceDimension
T2 L+2 M+1 I2 Θ0 N0 J0
InductanceDimension
T+1 L0 M0 I+1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/ElementaryCharge
http://dbpedia.org/page/Elementary_charge
The magnitude of the electric charge carried by a single electron. It defines the base unit Ampere in the SI system.
https://physics.nist.gov/cgibin/cuu/Value?e
https://doi.org/10.1351/goldbook.E02032
The DBpedia definition (http://dbpedia.org/page/Elementary_charge) is outdated as May 20, 2019. It is now an exact quantity.
ElementaryCharge
T+3 L1 M1 I0 Θ0 N0 J+1
LuminousEfficacyDimension
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/RefractiveIndex
http://dbpedia.org/page/Refractive_index
https://doi.org/10.1351/goldbook.R05240
Factor by which the phase velocity of light is reduced in a medium.
RefractiveIndex
T+4 L3 M1 I+2 Θ0 N0 J0
http://qudt.org/vocab/constant/PermittivityOfVacuum
https://physics.nist.gov/cgibin/cuu/Value?ep0
https://doi.org/10.1351/goldbook.P04508
The DBpedia definition (http://dbpedia.org/page/Vacuum_permittivity) is outdated since May 20, 2019. It is now a measured constant.
The value of the absolute dielectric permittivity of classical vacuum.
VacuumElectricPermittivity
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Work
http://dbpedia.org/page/Heat
http://dbpedia.org/page/Work_(physics)
Product of force and displacement.
https://doi.org/10.1351/goldbook.W06684
Work
T0 L2 M0 I0 Θ0 N0 J+1
IlluminanceDimension
T1 L0 M0 I0 Θ0 N+1 J0
http://dbpedia.org/page/Temperature
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.
https://doi.org/10.1351/goldbook.T06261
CelsiusTemperature
T1 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/AngularMomentum
http://dbpedia.org/page/Angular_momentum
https://doi.org/10.1351/goldbook.A00353
Measure of the extent and direction an object rotates about a reference point.
AngularMomentum
T3 L+2 M+1 I2 Θ0 N0 J0
ElectricResistanceDimension
T1 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/constant/PlanckConstant
http://dbpedia.org/page/Planck_constant
The quantum of action. It defines the kg base unit in the SI system.
https://physics.nist.gov/cgibin/cuu/Value?h
https://doi.org/10.1351/goldbook.P04685
PlanckConstant
T0 L0 M+1 I0 Θ0 N0 J0
MassDimension
T3 L+2 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Impedance
http://dbpedia.org/page/Electrical_impedance
Measure of the opposition that a circuit presents to a current when a voltage is applied.
Impedance
ElectricImpedance
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MassFraction
http://dbpedia.org/page/Mass_fraction_(chemistry)
http://www.ontologyofunitsofmeasure.org/resource/om2/MassFraction
https://doi.org/10.1351/goldbook.M03722
Mass of a constituent divided by the total mass of all constituents in the mixture.
MassFraction
T0 L2 M0 I+1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/ElectricCurrentDensity
http://dbpedia.org/page/Current_density
https://doi.org/10.1351/goldbook.E01928
Electric current divided by the crosssectional area it is passing through.
CurrentDensity
T1 L+1 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Speed
http://dbpedia.org/page/Speed
http://www.ontologyofunitsofmeasure.org/resource/om2/Speed
https://doi.org/10.1351/goldbook.S05852
Length per unit time.
Speed in the absolute value of the velocity.
Speed
T0 L0 M0 I0 Θ0 N+1 J0
http://qudt.org/vocab/quantitykind/AmountOfSubstance
http://dbpedia.org/page/Amount_of_substance
The number of elementary entities present.
https://doi.org/10.1351/goldbook.A00297
"In the name “amount of substance”, the word “substance” will typically be replaced by words to specify the substance concerned in any particular application, for example “amount of hydrogen chloride, HCl”, or “amount of benzene, C6H6 ”. It is important to give a precise definition of the entity involved (as emphasized in the definition of the mole); this should preferably be done by specifying the molecular chemical formula of the material involved. Although the word “amount” has a more general dictionary definition, the abbreviation of the full name “amount of substance” to “amount” may be used for brevity."
 SI Brochure
AmountOfSubstance
T0 L+2 M0 I+1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MagneticDipoleMoment
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1211155
http://dbpedia.org/page/Magnetic_moment
109.1
Vector quantity μ causing a change to its energy ΔW in an external magnetic field of field flux density B:
ΔW = −μ · B
http://goldbook.iupac.org/terms/view/M03688
For an atom or nucleus, this energy is quantized and can be written as:
W = g μ M B
where g is the appropriate g factor, μ is mostly the Bohr magneton or nuclear magneton, M is magnetic quantum number, and B is magnitude of the magnetic flux density.
 ISO 80000
MagneticDipoleMoment
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/InternalEnergy
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130420
http://dbpedia.org/page/Internal_energy
A state quantity equal to the difference between the total energy of a system and the sum of the macroscopic kinetic and potential energies of the system.
http://www.ontologyofunitsofmeasure.org/resource/om2/InternalEnergy
https://doi.org/10.1351/goldbook.I03103
ThermodynamicEnergy
InternalEnergy
T2 L+2 M0 I0 Θ0 N0 J0
AbsorbedDoseDimension
T1 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Frequency
http://dbpedia.org/page/Frequency
Number of periods per time interval.
https://doi.org/10.1351/goldbook.FT07383
Frequency
T2 L+2 M+1 I0 Θ0 N1 J0
http://qudt.org/vocab/quantitykind/ChemicalPotential
http://dbpedia.org/page/Chemical_potential
https://doi.org/10.1351/goldbook.C01032
Energy per unit change in amount of substance.
ChemicalPotential
T1 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/SpecificActivity
Decays per unit time.
https://doi.org/10.1351/goldbook.A00114
Radioactivity
T0 L0 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/constant/ProtonMass
https://physics.nist.gov/cgibin/cuu/Value?mp
https://doi.org/10.1351/goldbook.P04914
The rest mass of a proton.
ProtonMass
T2 L+2 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/AbsorbedDose
http://dbpedia.org/page/Absorbed_dose
Energy imparted to matter by ionizing radiation in a suitable small element of volume divided by the mass of that element of volume.
https://doi.org/10.1351/goldbook.A00031
AbsorbedDose
T0 L+3 M0 I0 Θ0 N0 J0
VolumeDimension
T3 L+2 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Reactance
http://dbpedia.org/page/Electrical_reactance
The opposition of a circuit element to a change in current or voltage, due to that element's inductance or capacitance.
Reactance
ElectricReactance
T2 L0 M+1 I1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MagneticFluxDensity
http://dbpedia.org/page/Magnetic_field
Strength of the magnetic field.
https://doi.org/10.1351/goldbook.M03686
Often denoted B.
MagneticFluxDensity
T0 L+2 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Area
http://dbpedia.org/page/Area
https://doi.org/10.1351/goldbook.A00429
Extent of a surface.
Area
T0 L2 M0 I0 Θ0 N0 J+1
http://qudt.org/vocab/quantitykind/Luminance
http://dbpedia.org/page/Luminance
https://doi.org/10.1351/goldbook.L03640
Measured in cd/m². Not to confuse with Illuminance, which is measured in lux (cd sr/m²).
a photometric measure of the luminous intensity per unit area of light travelling in a given direction.
Luminance
T1 L+1 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/constant/SpeedOfLight_Vacuum
http://dbpedia.org/page/Speed_of_light
The speed of light in vacuum. Defines the base unit metre in the SI system.
https://physics.nist.gov/cgibin/cuu/Value?c
https://doi.org/10.1351/goldbook.S05854
SpeedOfLightInVacuum
T+4 L2 M1 I+2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Capacitance
http://dbpedia.org/page/Capacitance
The derivative of the electric charge of a system with respect to the electric potential.
https://doi.org/10.1351/goldbook.C00791
ElectricCapacitance
Capacitance
T2 L+2 M+1 I0 Θ1 N0 J0
http://qudt.org/vocab/quantitykind/Entropy
http://dbpedia.org/page/Entropy
https://doi.org/10.1351/goldbook.E02149
Logarithmic measure of the number of available states of a system.
May also be referred to as a measure of order of a system.
Entropy
T0 L+1 M0 I0 Θ0 N0 J0
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130312
http://dbpedia.org/page/Center_of_mass
The unique point where the weighted relative position of the distributed mass of an Item sums to zero. Equivalently, it is the point where if a force is applied to the Item, causes the Item to move in direction of force without rotation.
https://en.wikipedia.org/wiki/Center_of_mass
In nonrelativistic physics, the centre of mass doesn’t depend on the chosen reference frame.
CentreOfMass
T0 L1 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/constant/RydbergConstant
http://dbpedia.org/page/Rydberg_constant
https://physics.nist.gov/cgibin/cuu/Value?ryd
https://doi.org/10.1351/goldbook.R05430
The Rydberg constant represents the limiting value of the highest wavenumber (the inverse wavelength) of any photon that can be emitted from the hydrogen atom, or, alternatively, the wavenumber of the lowestenergy photon capable of ionizing the hydrogen atom from its ground state.
RybergConstant
T0 L0 M0 I0 Θ0 N0 J0
http://dbpedia.org/page/Dimensionless_quantity
A quantity to which no physical dimension is assigned and with a corresponding unit of measurement in the SI of the unit one.
https://en.wikipedia.org/wiki/Dimensionless_quantity
https://doi.org/10.1351/goldbook.D01742
ISQDimensionlessQuantity
T0 L0 M0 I0 Θ+1 N0 J0
TemperatureDimension
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/VolumeFraction
http://dbpedia.org/page/Volume_fraction
Volume of a constituent of a mixture divided by the sum of volumes of all constituents prior to mixing.
http://www.ontologyofunitsofmeasure.org/resource/om2/VolumeFraction
https://doi.org/10.1351/goldbook.V06643
VolumeFraction
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Torque
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130326
http://dbpedia.org/page/Torque
The effectiveness of a force to produce rotation about an axis, measured by the product of the force and the perpendicular distance from the line of action of the force to the axis.
http://www.ontologyofunitsofmeasure.org/resource/om2/Torque
https://doi.org/10.1351/goldbook.T06400
Even though torque has the same physical dimension as energy, it is not of the same kind and can not be measured with energy units like joule or electron volt.
Torque
T+1 L0 M0 I+1 Θ0 N0 J0
ElectricChargeDimension
T2 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/KineticEnergy
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130349
http://dbpedia.org/page/Kinetic_energy
The energy of an object due to its motion.
http://www.ontologyofunitsofmeasure.org/resource/om2/KineticEnergy
https://doi.org/10.1351/goldbook.K03402
KineticEnergy
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Strain
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130357
Change of the relative positions of parts of a body, excluding a displacement of the body as a whole.
http://www.ontologyofunitsofmeasure.org/resource/om2/Strain
Strain
T2 L+2 M+1 I0 Θ1 N1 J0
http://qudt.org/vocab/constant/MolarGasConstant
http://dbpedia.org/page/Gas_constant
Equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole (rather than energy per temperature increment per particle).
https://physics.nist.gov/cgibin/cuu/Value?r
https://doi.org/10.1351/goldbook.G02579
MolarGasConstant
T0 L0 M0 I0 Θ0 N1 J0
PerAmountDimension
T0 L2 M+1 I0 Θ0 N0 J0
http://dbpedia.org/page/Area_density
https://doi.org/10.1351/goldbook.S06167
Mass per unit area.
AreaDensity
T0 L0 M0 I0 Θ+1 N0 J0
qudt.org/vocab/quantitykind/ThermodynamicTemperature
http://dbpedia.org/page/Thermodynamic_temperature
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.
https://doi.org/10.1351/goldbook.T06321
ThermodynamicTemperature
T+4 L2 M1 I+2 Θ0 N0 J0
CapacitanceDimension
T0 L+1 M0 I0 Θ0 N0 J0
LengthDimension
T0 L1 M0 I+1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MagneticFieldStrength
http://dbpedia.org/page/Magnetic_field
https://doi.org/10.1351/goldbook.M03683
Strength of a magnetic field. Commonly denoted H.
MagneticFieldStrength
T0 L2 M0 I0 Θ0 N0 J+1
http://qudt.org/vocab/quantitykind/Illuminance
http://dbpedia.org/page/Illuminance
The total luminous flux incident on a surface, per unit area.
https://doi.org/10.1351/goldbook.I02941
Illuminance
T+2 L1 M1 I+1 Θ0 N0 J0
http://qudt.org/vocab/constant/JosephsonConstant
Inverse of the magnetic flux quantum.
https://physics.nist.gov/cgibin/cuu/Value?kjos
The DBpedia definition (http://dbpedia.org/page/Magnetic_flux_quantum) is outdated as May 20, 2019. It is now an exact quantity.
JosephsonConstant
T0 L0 M0 I0 Θ0 N0 J0
A pure number, typically the number of something.
1,
i,
π,
the number of protons in the nucleus of an atom
According to the SI brochure counting does not automatically qualify a quantity as an amount of substance.
This quantity is used only to describe the outcome of a counting process, without regard of the type of entities.
"There are also some quantities that cannot be described in terms of the seven base quantities of the SI, but have the nature of a count. Examples are a number of molecules, a number of cellular or biomolecular entities (for example copies of a particular nucleic acid sequence), or degeneracy in quantum mechanics. Counting quantities are also quantities with the associated unit one."
PureNumberQuantity
T1 L0 M0 I0 Θ0 N+1 J0
http://qudt.org/vocab/quantitykind/CatalyticActivity
Increase in the rate of reaction of a specified chemical reaction that an enzyme produces in a specific assay system.
https://doi.org/10.1351/goldbook.C00881
CatalyticActivity
T3 L+2 M+1 I0 Θ0 N0 J0
PowerDimension
T0 L0 M0 I+1 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/ElectricCurrent
http://dbpedia.org/page/Electric_current
A flow of electric charge.
https://doi.org/10.1351/goldbook.E01927
ElectricCurrent
T+1 L0 M0 I+1 Θ0 N0 J0
The charge of an electron.
https://doi.org/10.1351/goldbook.E01982
The negative of ElementaryCharge.
ElectronCharge
T0 L+1 M0 I0 Θ0 N0 J0
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130119
http://dbpedia.org/page/Length
Extend of a spatial dimension.
https://doi.org/10.1351/goldbook.L03498
Length is a nonnegative additive quantity attributed to a onedimensional object in space.
Length
T+3 L3 M1 I+2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/ElectricConductivity
http://dbpedia.org/page/Electrical_resistivity_and_conductivity
https://doi.org/10.1351/goldbook.C01245
Measure of a material's ability to conduct an electric current.
Conductivity is equeal to the resiprocal of resistivity.
Conductivity
ElectricConductivity
T1 L0 M0 I0 Θ0 N+1 J0
CatalyticActivityDimension
T2 L1 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Stress
http://dbpedia.org/page/Stress_(mechanics)
Force per unit oriented surface area .
Measure of the internal forces that neighboring particles of a continuous material exert on each other.
Stress
T+1 L0 M0 I0 Θ0 N0 J0
qudt.org/vocab/quantitykind/Time
http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=1130103
http://dbpedia.org/page/Time
Onedimensional subspace of spacetime, which is locally orthogonal to space.
The indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.
https://doi.org/10.1351/goldbook.T06375
Time can be seen as the duration of an event or, more operationally, as "what clocks read".
Time
T0 L3 M0 I0 Θ0 N+1 J0
http://qudt.org/vocab/quantitykind/AmountOfSubstanceConcentrationOfB
http://dbpedia.org/page/Molar_concentration
https://doi.org/10.1351/goldbook.A00295
The amount of a constituent divided by the volume of the mixture.
Concentration
MolarConcentration
Molarity
AmountConcentration
T0 L0 M0 I+1 Θ0 N0 J0
ElectricCurrentDimension
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/constant/FineStructureConstant
http://dbpedia.org/page/Finestructure_constant
https://physics.nist.gov/cgibin/cuu/Value?alph
https://doi.org/10.1351/goldbook.F02389
A fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles.
FineStructureConstant
T0 L1 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Wavenumber
http://dbpedia.org/page/Wavenumber
http://www.ontologyofunitsofmeasure.org/resource/om2/Wavenumber
https://doi.org/10.1351/goldbook.W06664
The number of waves per unit length along the direction of propagation.
Wavenumber
T2 L+3 M1 I0 Θ0 N0 J0
http://qudt.org/vocab/constant/NewtonianConstantOfGravitation
http://dbpedia.org/page/Gravitational_constant
https://physics.nist.gov/cgibin/cuu/Value?bg
https://doi.org/10.1351/goldbook.G02695
Physical constant in Newton's law of gravitation and in Einstein's general theory of relativity.
NewtonianConstantOfGravity
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/MassNumber
Number of nucleons in an atomic nucleus.
AtomicMassNumber
NucleonNumber
MassNumber
T2 L+1 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/constant/ElectromagneticPermeabilityOfVacuum
https://physics.nist.gov/cgibin/cuu/Value?mu0
The DBpedia and UIPAC Gold Book definitions (http://dbpedia.org/page/Vacuum_permeability, https://doi.org/10.1351/goldbook.P04504) are outdated since May 20, 2019. It is now a measured constant.
The value of magnetic permeability in a classical vacuum.
VacuumMagneticPermeability
T3 L+3 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Resistivity
http://dbpedia.org/page/Electrical_resistivity_and_conductivity
https://doi.org/10.1351/goldbook.R05316
Electric field strength divided by the current density.
Resistivity
ElectricResistivity
T0 L0 M0 I0 Θ0 N0 J+1
http://qudt.org/vocab/quantitykind/LuminousFlux
http://dbpedia.org/page/Luminous_flux
Perceived power of light.
https://doi.org/10.1351/goldbook.L03646
LuminousFlux
T2 L+1 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Acceleration
http://dbpedia.org/page/Acceleration
https://doi.org/10.1351/goldbook.A00051
Derivative of velocity with respect to time.
Acceleration
T3 L+2 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/RadiantFlux
http://dbpedia.org/page/Radiant_flux
https://doi.org/10.1351/goldbook.R05046
The radiant energy emitted, reflected, transmitted or received, per unit time.
RadiantFlux
T0 L0 M0 I0 Θ0 N+1 J0
AmountDimension
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/SolidAngle
http://dbpedia.org/page/Solid_angle
Ratio of area on a sphere to its radius squared.
https://doi.org/10.1351/goldbook.S05732
SolidAngle
T3 L+2 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Resistance
http://dbpedia.org/page/Electrical_resistance_and_conductance
Measure of the difficulty to pass an electric current through a material.
https://doi.org/10.1351/goldbook.E01936
Inverse of 'ElectricalConductance'.
Resistance
ElectricResistance
T3 L+2 M+1 I2 Θ0 N0 J0
http://qudt.org/vocab/constant/VonKlitzingConstant
The von Klitzing constant is defined as Planck constant divided by the square of the elementary charge.
https://physics.nist.gov/cgibin/cuu/Value?rk
Resistance quantum.
VonKlitzingConstant
T2 L0 M+1 I1 Θ0 N0 J0
MagneticFluxDensityDimension
T0 L1 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/InverseLength
http://dbpedia.org/page/Reciprocal_length
The inverse of length.
https://en.wikipedia.org/wiki/Reciprocal_length
InverseLength
ReciprocalLength
T0 L0 M+1 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Mass
http://dbpedia.org/page/Mass
Property of a physical body that express its resistance to acceleration (a change in its state of motion) when a force is applied.
https://doi.org/10.1351/goldbook.M03709
Mass
T0 L3 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Volume
http://dbpedia.org/page/Volume
Extent of an object in space.
Volume
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.
SIExactConstant
Quantities declared under the ISO 80000.
https://en.wikipedia.org/wiki/International_System_of_Quantities
https://www.iso.org/obp/ui/#iso:std:iso:80000:1:ed1:v1:en:sec:3.1
InternationalSystemOfQuantity
T0 L0 M0 I0 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/PlaneAngle
http://dbpedia.org/page/Angle
Ratio of circular arc length to radius.
https://doi.org/10.1351/goldbook.A00346
PlaneAngle
Angle
T2 L+2 M+1 I0 Θ0 N0 J0
EnergyDimension
T1 L+1 M0 I0 Θ0 N0 J0
VelocityDimension
T1 L0 M0 I0 Θ0 N0 J0
The frequency standard in the SI system in which the photon absorption by transitions between the two hyperfine ground states of caesium133 atoms are used to control the output frequency.
It defines the base unit second in the SI system.
https://physics.nist.gov/cgibin/cuu/Value?nucs
HyperfineTransitionFrequencyOfCs
T0 L0 M0 I0 Θ0 N0 J0
The class of quantities that are the ratio of two quantities with the same physical dimensionality.
refractive index,
volume fraction,
fine structure constant
Quantities defined as ratios `Q=A/B` having equal dimensions in numerator and denominator are dimensionless quantities but still have a physical dimension defined as dim(A)/dim(B).
Johansson, Ingvar (2010). "Metrological thinking needs the notions of parametric quantities, units and dimensions". Metrologia. 47 (3): 219–230. doi:10.1088/00261394/47/3/012. ISSN 00261394.
https://iopscience.iop.org/article/10.1088/00261394/47/3/012
RatioQuantity
T+3 L2 M1 I+2 Θ0 N0 J0
http://qudt.org/vocab/quantitykind/Conductance
http://dbpedia.org/page/Electrical_resistance_and_conductance
Measure of the ease for electric current to pass through a material.
https://doi.org/10.1351/goldbook.E01925
Inverse of 'ElectricalResistance'.
Conductance
ElectricConductance
T2 L+2 M+1 I0 Θ1 N0 J0
http://qudt.org/vocab/constant/BoltzmannConstant
http://dbpedia.org/page/Boltzmann_constant
A physical constant relating energy at the individual particle level with temperature. It is the gas constant R divided by the Avogadro constant.
It defines the Kelvin unit in the SI system.
https://physics.nist.gov/cgibin/cuu/Value?k
https://doi.org/10.1351/goldbook.B00695
The DBpedia definition (http://dbpedia.org/page/Boltzmann_constant) is outdated as May 20, 2019. It is now an exact quantity.
BoltzmannConstant
An engineered object which is instrumental for reaching a particular purpose through its characteristic functioning process, with particular reference to mechanical or electronic equipment.
From Old French "deviser", meaning: arrange, plan, contrive.
Literally "dispose in portions," from Vulgar Latin "divisare", frequentative of Latin dividere, meaning "to divide"
Device
A manufacturing process whose product is the result of the combination of more substances.
Synthesis of materials, the preparation of a cake.
ContinuumManufacturing
A 'physical' that stands for a real world object that has been designed and manufactured for a particular purpose.
Car, tire, composite material.
The 'Engineered' branch represents real world objects that show some level of complexity/heterogeneity in their composition, and are made for a specific use.
Engineered
A manufacturing process aimed to the production of a device made of specific components.
Assemblying a bicycle, building a car.
DiscreteManufacturing
The process of transforming raw materials into a product by the use of manual labor, machinery or chemical/biological processes.
From Latin manufacture: "made by hand".
Manufacturing
A material that is synthesized within a manufacturing process.
EngineeredMaterial
Gas is a compressible fluid, a state of matter that has no fixed shape and no fixed volume.
Gas
A material in which distributed particles of one phase are dispersed in a different continuous phase.
Dispersion
A mixture in which more than one phases of matter cohexists.
Phase heterogenous mixture may share the same state of matter.
For example, immiscibile liquid phases (e.g. oil and water) constitute a mixture whose phases are clearly separated but share the same state of matter.
PhaseHeterogeneousMixture
A single phase mixture.
PhaseHomogeneousMixture
A 'spacetime' that stands for a quantum system made of electrons.
ElectronCloud
Nanomaterials are Materials possessing all external dimension measuring 1100nm
NanoParticle
A colloid formed by trapping pockets of gas in a liquid or solid.
Foam
A solution is a homogeneous mixture composed of two or more substances.
Solutions are characterized by the occurrence of Rayleigh scattering on light,
Solution
A coarse dispersion of solid in a solid continuum phase.
Granite, sand, dried concrete.
SolidSolidSuspension
An atom that does not share electrons with other atoms.
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.
StandaloneAtom
A colloid in which small particles (1 nm to 100 nm) are suspended in a continuum phase.
Sol
An atom_based state defined by an exact number of ebonded atomic species and an electron cloud made of the shared electrons.
H20, C6H12O6, CH4
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 nonperiodic 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
A coarse dispersion of liquid in a solid continuum phase.
SolidLiquidSuspension
A soft, solid or solidlike colloid consisting of two or more components, one of which is a liquid, present in substantial quantity.
Gel
An emulsion is a mixture of two or more liquids that are normally immiscible (a liquidliquid heterogeneous mixture).
Mayonnaise, milk.
Emulsion
A coarse dispersion of gas in a liquid continuum phase.
Sparkling water
LiquidGasSuspension
A type of sol in the form of one solid dispersed in liquid.
LiquidSol
A standalone atom that has no net charge.
NeutralAtom
A coarse dispersion of liquid in a liquid continuum phase.
LiquidLiquidSuspension
A suspension of liquid droplets dispersed in a gas through an atomization process.
Spray
An heterogeneous mixture that contains coarsly dispersed particles (no Tyndall effect), that generally tend to separate in time to the dispersion medium phase.
Suspensions show no significant effect on light.
Suspension
A liquid solution made of two or more component substances.
LiquidSolution
A fluid in which a gas is ionized to a level where its electrical conductivity allows longrange electric and magnetic fields to dominate its behaviour.
Plasma
A liquid aerosol composed of water droplets in air or another gas.
Vapor
Nucleon
A colloid composed of fine solid particles or liquid droplets in air or another gas.
Aerosol
Smoke is a solid aerosol made of particles emitted when a material undergoes combustion or pyrolysis.
Smoke
A type of sol in the form of one solid dispersed in another continuous solid.
SolidSol
A gaseous solution made of more than one component type.
GasMixture
A liquid solution in which the solvent is water.
AcqueousSolution
Nanomaterials are Materials possessing, at minimum, one external dimension measuring 1100nm
NanoMaterial
A solid solution made of two or more component substances.
SolidSolution
A matter object throughout which all physical properties of a material are essentially uniform.
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase.
The term phase is sometimes used as a synonym for state of matter, but there can be several immiscible phases of the same state of matter. Also, the term phase is sometimes used to refer to a set of equilibrium states demarcated in terms of state variables such as pressure and temperature by a phase boundary on a phase diagram. Because phase boundaries relate to changes in the organization of matter, such as a change from liquid to solid or a more subtle change from one crystal structure to another, this latter usage is similar to the use of "phase" as a synonym for state of matter. However, the state of matter and phase diagram usages are not commensurate with the formal definition given above and the intended meaning must be determined in part from the context in which the term is used.
[https://en.wikipedia.org/wiki/Phase_(matter)]
PhaseOfMatter
A material that undergoes chemical changes.
ReactiveMaterial
A mixture in which one substance of microscopically dispersed insoluble or soluble particles (from 1 nm to 1 μm) is suspended throughout another substance and that does not settle, or would take a very long time to settle appreciably.
Colloids are characterized by the occurring of the Tyndall effect on light.
Colloid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure.
Liquid
A Material occurring in nature, without the need of human intervention.
NaturalMaterial
Subatomic
An bonded atom that shares at least one electron to the atombased entity of which is part of.
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 unentangled with the inner shells of the atoms composing the molecule.
BondedAtom
A continuum that has no fixed shape and yields easily to external pressure.
Gas, liquid, plasma,
Fluid
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
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
Proton
An aerosol composed of liquid droplets in air or another gas.
LiquidAerosol
An aerosol composed of fine solid particles in air or another gas.
SolidAerosol
A foam of trapped gas in a solid.
Aerogel
SolidFoam
A continuum characterized by structural rigidity and resistance to changes of shape or volume, that retains its shape and density when not confined.
Solid
A superclass made as the disjoint union of all the form under which matter can exist.
In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma.
https://en.wikipedia.org/wiki/State_of_matter
StateOfMatter
A coarse dispersion of gas in a solid continuum phase.
SolidGasSuspension
A coarse dispersion of solid in a gas continuum phase.
Dust, sand storm.
GasSolidSuspension
A foam of trapped gas in a liquid.
LiquidFoam
A standalone atom with an unbalanced number of electrons with respect to its atomic number.
The ion_atom is the basic part of a pure ionic bonded compound i.e. without eclectron sharing,
IonAtom
Neutron
A coarse dispersion of liquid in a gas continuum phase.
Rain, spray.
GasLiquidSuspension
A suspension of fine particles in the atmosphere.
Dust
A coarse dispersion of solids in a liquid continuum phase.
Mud
LiquidSolidSuspension
A standalone atom has direct part one 'nucleus' and one 'electron_cloud'.
An O 'atom' within an O2 'molecule' is an 'ebonded_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.
An 'atom' is a 'nucleus' surrounded by an 'electron_cloud', i.e. a quantum system made of one or more bounded electrons.
Atom
A Miixture is a material made up of two or more different substances which are physically (not chemically) combined.
Mixture
Nucleus
Δ
Laplacian
Vector
A relation which makes a nonequal comparison between two numbers or other mathematical expressions.
f(x) > 0
Inequality
1
Real
2x+3
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)
AlgebricExpression
Matrix
A 'Variable' is a symbolic object that stands for a numerical defined 'Mathematical' object like e.g. a number, a vector, a matrix.
x
k
Variable
A numerical data value.
A number is actually a string (e.g. 1.4, 1e8) 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.
In math usually number and numeral are distinct concepts, the numeral being the symbol or a composition of symbols (e.g. 3.14, 010010, three) and the number is the idea behind it.
More than one numeral stand for the same number.
In the EMMO abstract entities does not exists, and numbers are simply defined by other numerals, so that a number is the class of all the numerals that are equivalent (e.g. 3 and 0011 are numerals that stands for the same number).
Or alternatively, an integer numeral may also stands for a set of a specific cardinality (e.g. 3 stands for a set of three apples). Rational and real numbers are simply a syntactic arrangment of integers (digits, in decimal system).
The fact that you can't give a name to a number without using a numeral or, in case of positive integers, without referring to a real world objects set with specific cardinality, suggests that the abstract concept of number is not a concept that can be practically used.
For these reasons, the EMMO will consider numerals and numbers as the same concept.
Number
Exponent
An equation that define a new variable in terms of other mathematical entities.
The definition of velocity as v = dx/dt.
The definition of density as mass/volume.
y = f(x)
DefiningEquation
*
Multiplication
AlgebricOperator

Minus
A function defined using functional notation.
y = f(x)
FunctionDefinition
A 'Mathematical' that has no unknown value, i.e. all its 'Variable"s parts refers to a 'Number' (for scalars that have a builtin datatype) or to another 'Numerical' (for complex numerical data structures that should rely on external implementations).
Numerical
=
The equals symbol.
Equals
1
Boolean
The class of general mathematical symbolic objects respecting mathematical syntactic rules.
Mathematical
MathematicalSymbol
ArithmeticOperator
A mathematical string that can be evaluated as true or false.
MathematicalFormula
2+2
ArithmeticExpression
+
Plus
2 * x^2 + x + 3
Polynomial
2 * a  b = c
An 'equation' that has parts two 'polynomial's
AlgebricEquation
/
Division
1 + 1 = 2
ArithmeticEquation
A 'varaible' that stand for a well known constant.
π refers to the constant number ~3.14
Constant
∇
Gradient
viscosity in the NavierStokes equation
A 'variable' whose value is assumed to be known independently from the equation, but whose value is not explicitated in the equation.
Parameter
The class of 'mathematical's that stand for a statement of equality between two mathematical expressions.
2+3 = 5
x^2 +3x = 5x
dv/dt = a
sin(x) = y
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.
Equation
MathematicalOperator
DifferentialOperator
1
Integer
A wellformed finite combination of mathematical symbols according to some specific rules.
Expression
The dependent variable for which an equation has been written.
Velocity, for the NavierStokes equation.
Unknown
Array
A 'Mathematical' entity that is made of a 'Numeral' 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.
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 800001
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.
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).
— 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 800001
PhysicalQuantity
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.
DerivedUnit
IdiomaticSymbol
A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of such.
International vocabulary of metrology (VIM)
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).
ReferenceUnit
A symbol that stands for a single unit.
Some examples are "Pa", "m" and "J".
UnitSymbol
T0 L0 M0 I0 Θ0 N0 J0
"The unit one is the neutral element of any system of units – necessary and present automatically."
SI Brochure
DimensionOne
A unit symbol that stands for a derived unit.
Pa stands for N/m2
J stands for N m
Special units are semiotic shortcuts to more complex composed symbolic objects.
SpecialUnit
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.
MeasuredConstant
A symbol that stands for a concept in the language of the meterological domain of ISO 80000.
MetrologicalSymbol
A unit that does not belong to any system of units.
eV
barn
OffSystemUnit
http://qudt.org/vocab/unit/UNITLESS
Represents the number 1, used as an explicit unit to say something has no units.
Refractive index or volume fraction.
Typically used for ratios of two units whos dimensions cancels out.
UnitOne
Measurement unit obtained by multiplying a given measurement unit by an integer greater than one.
MultipleUnit
"Quantity, in a system of quantities, defined in terms of the base quantities of that system".
DerivedQuantity
Dimensionless multiplicative unit prefix.
https://en.wikipedia.org/wiki/Metric_prefix
MetricPrefix
A measurement unit symbol that do not have a metric prefix as a direct spatial part.
NonPrefixedUnit
Physical constant used to define a unit system. Hence, when expressed in that unit system they have an exact value with no associated uncertainty.
ExactConstant
A language object used in metrology.
Metrology includes all theoretical and practical aspects of measurement, whatever the measurement uncertainty and field of application.
 International vocabulary of metrology (VIM)
This language domain makes use of ISO 80000 concepts.
Metrological
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.
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)
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 800001
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([+][19]0) L([+][19]0) M([+][19]0) I([+][19]0) Θ([+][19]0) N([+][19]0) J([+][19]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 M2 I+1 Θ0 N0 J0
PhysicalDimension
Measurement unit obtained by dividing a given measurement unit by an integer greater than one.
SubMultipleUnit
"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 800001
BaseQuantity
A reference unit provided by a reference material.
International vocabulary of metrology (VIM)
Arbitrary amountofsubstance concentration of lutropin in a given sample of plasma (WHO international standard 80/552): 5.0 International Unit/l
StandardUnit
1
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'.
"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 800001
"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/sibrochure/SIBrochure9EN.pdf
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'.
MeasurementUnit
https://en.wikipedia.org/wiki/List_of_physical_constants
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.
PhysicalConstant
"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)
Hardness
Resilience
"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)
OrdinalQuantity
1
1
A measurement unit that is made of a metric prefix and a unit symbol.
PrefixedUnit
A reference unit provided by a measurement procedure.
Rockwell C hardness of a given sample (150 kg load): 43.5HRC(150 kg)
ProcedureUnit
A set of units that correspond to the base quantities in a system of units.
BaseUnit
"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 800001
"A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of such."
International vocabulary of metrology (VIM)
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.
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.
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).
QuantitativeProperty
1
1
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).
6.8 m
0.9 km
8 K
6 MeV
43.5 HRC(150 kg)
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.
Referred as Quantity Value in International vocabulary of metrology (VIM)
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'.
Quantity
An experiment is a process that is intended to replicate a physical phenomenon in a controlled environment.
Experiment
An 'equation' that stands for a 'physical_law' by mathematically defining the relations between physics_quantities.
The Newton's equation of motion.
The Schrödinger equation.
The NavierStokes equation.
PhysicsEquation
A 'process' that is recognized by physical sciences and is catogrized accordingly.
While every 'process' in the EMMO involves physical objects, this class is devoted to represent real world objects that express a phenomenon relevant for the ontologist.
PhysicalPhenomenon
A physicsbased model based on a physics equation describing the behaviour of continuum volume.
ContinuumModel
A physicsbased 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.
MesoscopicModel
The 'semiosis' process of interpreting a 'physical' and provide a complec sign, 'theory' that stands for it and explain it to another interpreter.
Theorization
A physicsbased model based on a physics equation describing the behaviour of electrons.
Density functional theory.
HartreeFock.
ElectronicModel
A physicsbased model based on a physics equation describing the behaviour of atoms.
AtomisticModel
A 'conventional' that stand for a 'physical'.
The 'theory' is e.g. a proposition, a book or a paper whose subsymbols 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: legisignsymbolargument
Theory
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).
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
PhysicalLaw
A computational model that uses existing data to create new insight into the behaviour of a system.
DataBasedModel
A solvable set of one Physics Equation and one or more Materials Relations.
PhysicsBasedModel
NaturalLaw
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 LennardJones potential.
A force field.
An Hamiltonian.
A material_relation can e.g. return a predefined number, return a database query, be an equation that depends on other physics_quantities.
MaterialRelation
MaterialLaw
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
MathematicalModel
An 'Graphical' that stands for a token or a composition of tokens from one or more alphabets, without necessarily respecting syntactic rules.
fe780
emmo
!5*a
cat
for(i=0;i<N;++i)
Symbolic
Java
0manifold
1manifold
Curve
A 'Graphical' that stands for a real world object that shows a recognizable pictorial pattern without being necessarily associated to a symbolic language.
A drawing of a cat.
A circle on a paper sheet.
The Mona Lisa.
Pictorial
Plane
Point
Line
Spacing
3manifold
A language object that follows syntactic rules of a an idiom (e.g. english, italian).
Idiomatic
A 'Perceptual' which stands for a real world object whose spatiotemporal pattern makes it identifiable by an observer as a sound.
'acoustical' refers to the perception mechanism of the observer that can occur through a microphone, a ear.
Acoustical
A physical made of more than one symbol sequentially arranged.
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.
A string is made of concatenated symbols whose arrangement is onedimensional. Each symbol can have only one previous and one next neighborhood (bidirectional list).
A string is not requested to respect any syntactic rule: it's simply directly made of symbols.
String
EuclideanSpace
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 nonhuman).
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).
The metasemiotic 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 metalevel: 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.
'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
A 'Perceptual' is a metaobject, meaning that is addressed by the ontologist (the metainterpreter) in a metasemiotic 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.
From Latin perceptiō (“a receiving or collecting, perception, comprehension”), from perceptus (“perceived, observed”).
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).
Perceptual
A language object respectin the syntactic rules of C++.
C++
Numeral
Torus
A language object that follows syntactic rules of a programming language.
Software
A symbolic entity made of other symbolic entities according to a specific spatial configuration.
This class collects individuals that represents arrangements of strings, or other symbolic compositions, without any particular predifined arrangement schema.
SymbolicComposition
2manifold
The class of individuals that stand for an elementary mark of a specific symbolic code (alphabet).
The class of letter "A" is the symbol as idea and the letter A that you see on the screen is the mark.
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.
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
Punctuation
Python
Circle
A 'graphical' aimed to represent a geometrical concept.
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.
Geometrical
Letter
A 'Perceptual' which stands for a real world object whose spatial configuration shows a pattern identifiable by an observer.
'Graphical' objects include writings, pictures, sketches ...
From the Ancient Greek γραφή (graphḗ) which means drawing, painting, writing, a writing, description, and from γράφω (gráphō) which means scratch, carve.
Graphical
Sphere
A language object is a symbolic object respecting a specific language syntactic rules (a wellformed formula).
Language
UTF8
The class of individuals that stand for photons elementary particles.
Photon
The union of classes of elementary particles that possess mass.
Massive
A 'Physical' with no 'Massive' parts.
Vacuum
A matter individual that stands for a real world object representing an amount of a physical substance (or mixture of substances) in different states of matter or phases.
A instance of a material (e.g. nitrogen) can represent different states of matter. The fact that the individual also belongs to other classes (e.g. Gas) would reveal the actual form in which the material is found.
Material usually means some definite kind, quality, or quantity of matter, especially as intended for use.
Material
A 'Physical' that possesses some 'Massive' parts.
Matter
A 'Physical' with 'Massless' parts that are mediators of interactions.
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).
Field
The class of individuals that stand for quarks elementary particles.
Quark
The class of individuals that stand for gluons elementary particles.
Gluon
The class of individuals that stand for electrons elemntary particles.
Electron
The perspective for which physical objects are categorized only by concepts coming from applied physical sciences.
Physicalistic
The union of all classes categorizing elementary particles according to the Standard Model.
Only a subset of elementary particles from the Standard Model are here included for the sake of simplicity.
ElementaryParticle
The union of classes of elementary particles that do not possess mass.
Massless
The class of individuals that stand for gravitons elementary particles.
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.
Graviton
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.
Observation
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.
Observer
A 'Property' that cannot be univocally determined and depends on an agent (e.g. a human individual, a community) acting as blackbox.
The beauty of that girl.
The style of your clothing.
The word subjective means that a nonwell 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 nonwell 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.
SubjectiveProperty
A 'Property' that is determined by each 'Observer' following a well defined 'Observation' procedure through a specific perception channel.
The word objective does not mean that each observation will provide the same results. It means that the observation followed a well defined procedure.
This class refers to what is commonly known as physical property, i.e. a measurable property of physical system, whether is quantifiable or not.
ObjectiveProperty
An 'observation' that results in a quantitative comparison of a 'property' of an 'object' with a standard reference.
Measurement
MeasuredQuantitativeProperty
An 'ObjectiveProperty' 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
A color is a nominal property.
Sex of a human being.
"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)
NominalProperty
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)
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 hasProperty 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.
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.
We know real world entities through observation/perception.
A nonperceivable 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
ModelledQuantitativeProperty
A quantitative property attributed by agreement to a quantity for a given purpose.
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.
A property that is associated to an object by convention, or assumption.
ConventionalQuantitativeProperty
MeasurementInstrument
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 atomistic element (Elementary).
Direct parthood is the relation used to build the class hierarchy (and the granularity hierarchy) for this perspective.
Reductionistic
A 'Physical' which is a tessellation of spatial direct parts.
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.
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.
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'.
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' which is a tessellation of 'State' temporal direct parts.
'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 subpart objects, both in time and space).
'Existent' class collects all individuals that stand for physical objects that can be structured in well defined temporal subparts 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 nontransitivity 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.
An 'Existent' individual stands for a real world object for which the ontologist wants to 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 nontransitivity and inversefunctionality.
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.
exsistere (latin): to stay (to persist through time) outside others of the same type (to be distinct from the rest).
Existent
A 'Process', that has participant an 'Interpreter', that is aimed to produce a 'Sign' representing another participant, the 'Object'.
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
Semiosis
The entity (or agent, or observer, or cognitive entity) who connects 'Sign', 'Interpretant' and 'Object'.
Interpreter
The interpreter's internal representation of the object in a semiosis process.
Interpretant
A 'Sign' that stands for an 'Object' due to causal continguity.
Smoke stands for a combustion process (a fire).
My facial expression stands for my emotional status.
Index
A 'Sign' that stands for an 'Object' through convention, norm or habit, without any resemblance to it.
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
The object, in Peirce semiotics.
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
An 'Physical' that is used as sign ("semeion" in greek) that stands for another 'Physical' 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 atomistic '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.
A 'Sign' can have temporaldirectparts 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 atomistic 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
Sign
The class of individuals that stands for semiotic objects, i.e. objects that take part on a semiotic process.
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'
Semiotic
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.
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
Gy
http://qudt.org/vocab/unit/GRAY
https://doi.org/10.1351/goldbook.G02696
Measurement unit for absorbed dose.
Gray
1e12
p
Pico
W
http://qudt.org/vocab/unit/W
https://doi.org/10.1351/goldbook.W06656
Measurement unit for power.
Watt
1e1
d
Deci
A SI derived unit whos numerical factor in front of the product of SI base units is one.
m/s
kg/m^3
This class collects all units that are products or powers of SI base or SI special units only.
SICoherentDerivedUnit
1e1
da
Deka
1e2
h
Hecto
1e15
f
Femto
1e21
z
Zepto
K
http://qudt.org/vocab/unit/K
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.
https://doi.org/10.1351/goldbook.K03374
Kelvin
s
http://qudt.org/vocab/unit/SEC
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 groundstate hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.
https://doi.org/10.1351/goldbook.S05513
Second
SIUnitSymbol
kat
http://qudt.org/vocab/unit/KAT
https://doi.org/10.1351/goldbook.K03372
Measurement unit for catalytic activity.
Katal
The base units in the SI system.
https://www.bipm.org/utils/common/pdf/sibrochure/SIBrochure9EN.pdf
SIBaseUnit
1e12
T
Tera
1e18
a
Atto
1e15
P
Peta
SIMetricPrefix
Ω
http://qudt.org/vocab/unit/OHM
https://doi.org/10.1351/goldbook.O04280
Measurement unit for resistance.
Ohm
1e18
E
Exa
1e6
M
Mega
A derived unit whos numerical factor in front of the product of base units is NOT equal to one.
SINonCoherentDerivedUnit
C
http://qudt.org/vocab/unit/C
https://doi.org/10.1351/goldbook.C01365
Measurement unit for electric charge.
Coulomb
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.
SICoherentUnit
1e3
k
Kilo
m
http://qudt.org/vocab/unit/M
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.
https://doi.org/10.1351/goldbook.M03884
Metre
SINonCoherentUnit
J
http://qudt.org/vocab/unit/J
https://doi.org/10.1351/goldbook.J03363
Measurement unit for energy.
Joule
cd
http://qudt.org/vocab/unit/CD
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.
https://doi.org/10.1351/goldbook.C00787
Candela
kg
http://qudt.org/vocab/unit/KiloGM
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.
https://doi.org/10.1351/goldbook.K03391
Kilogram
1e6
µ
Micro
rad
http://qudt.org/vocab/unit/RAD
Measure of plane angle.
https://doi.org/10.1351/goldbook.R05036
Dimensionless measurement unit for plane angle.
Radian
1e3
m
Milli
Pa
http://qudt.org/vocab/unit/PA
https://doi.org/10.1351/goldbook.P04442
Measurement unit for pressure.
Pascal
1e9
G
Giga
F
http://qudt.org/vocab/unit/FARAD
https://doi.org/10.1351/goldbook.F02320
Measurement unit for electric capacitance.
Farad
N
http://qudt.org/vocab/unit/N
https://doi.org/10.1351/goldbook.N04135
Measurement unit for force.
Newton
T
http://qudt.org/vocab/unit/T
https://doi.org/10.1351/goldbook.T06283
Measurement unit for magnetic flux density or induction.
Tesla
°C
http://qudt.org/vocab/unit/DEG_C
https://doi.org/10.1351/goldbook.D01561
Measurement unit for Celsius temperature. This unit can only be used for expressing temperature differences.
DegreeCelsius
1e2
c
Centi
Bq
http://qudt.org/vocab/unit/BQ
Radioactive decays per second.
https://doi.org/10.1351/goldbook.B00624
Unit for radioactive activity.
Becquerel
sr
http://qudt.org/vocab/unit/SR
Dimensionless measurement unit for solid angle.
https://doi.org/10.1351/goldbook.S05971
Steradian
A SI base or special unit with a metric prefix.
The presence of the prefix makes this units noncoherent with SI system.
SIPrefixedUnit
lm
http://qudt.org/vocab/unit/LM
https://doi.org/10.1351/goldbook.L03639
Measurement unit for luminous flux.
Lumen
Wb
http://qudt.org/vocab/unit/WB
https://doi.org/10.1351/goldbook.W06666
Measurement unit for magnetic flux.
Weber
lx
http://qudt.org/vocab/unit/LUX
https://doi.org/10.1351/goldbook.L03651
Measurement unit for illuminance.
Lux
1e21
Z
Zetta
A
http://qudt.org/vocab/unit/A
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.
https://doi.org/10.1351/goldbook.A00300
Ampere
Sv
http://qudt.org/vocab/unit/SV
https://en.wikipedia.org/wiki/Equivalent_dose
https://doi.org/10.1351/goldbook.S05658
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.
Sievert
mol
http://qudt.org/vocab/unit/MOL
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.
https://doi.org/10.1351/goldbook.M03980
Mole
1e9
n
Nano
V
http://qudt.org/vocab/unit/V
https://doi.org/10.1351/goldbook.V06634
Measurement unit for voltage.
Volt
Hz
http://qudt.org/vocab/unit/HZ
https://doi.org/10.1351/goldbook.H02785
Measurement unit for frequence.
Hertz
1e24
Y
Yotta
The 22 derived units that are given a special name in the SI system that stands for units derived by SI base units.
https://en.wikipedia.org/wiki/International_System_of_Units#Derived_units
These units are SI coherent by definition.
SISpecialUnit
S
Measurement unit for electrical conductance.
Siemens
1e24
y
Yocto
H
http://qudt.org/vocab/unit/H
https://doi.org/10.1351/goldbook.H02782
Measurement unit for electrical inductance.
Henry
The set of units provided by the SI referring to the ISQ.
The complete set of SI units includes both the coherent set and the multiples and submultiples formed by using the SI prefixes.
The names, symbols and prefixes of SI units are defined by the General Conference on Weights and Measures (CGPM).
https://en.wikipedia.org/wiki/General_Conference_on_Weights_and_Measures
SIUnit
Da
http://qudt.org/vocab/unit/Dalton
http://dbpedia.org/page/Unified_atomic_mass_unit
One dalton is defined as one twelfth of the mass of an unbound neutral atom of carbon12 in its nuclear and electronic ground state.
https://doi.org/10.1351/goldbook.D01514
Dalton
au
http://qudt.org/vocab/unit/PARSEC
http://dbpedia.org/page/Astronomical_unit
One astronomical unit is defined as exactly 149597870700 m, which is roughly the distance from earth to sun.
https://en.wikipedia.org/wiki/Astronomical_unit
AstronomicalUnit
Unit for dimensionless units that cannot be expressed as a 'FractionUnit'.
Unit of AtomicNumber
PureNumberUnit
Unit for quantities of dimension one that are the fraction of two masses.
Unit for mass fraction.
MassFractionUnit
′
http://qudt.org/vocab/unit/ARCMIN
Measure of plane angle defined as 1/60 or a degree.
MinuteOfArc
ArcMinute
h
http://qudt.org/vocab/unit/HR
Measure of time defined as 3600 seconds.
https://doi.org/10.1351/goldbook.H02866
Hour
Å
http://qudt.org/vocab/unit/ANGSTROM
http://dbpedia.org/page/%C3%85ngstr%C3%B6m
Measure of length defined as 1e10 metres.
https://en.wikipedia.org/wiki/Angstrom
https://doi.org/10.1351/goldbook.N00350
Ångström is not mentioned in the SI system and deprecated by the International Bureau of Weights and Measures (BIPM).
Dispite of that, it is often used in the natural sciences and technology.
Angstrom
Ångström
d
http://qudt.org/vocab/unit/DAY
http://dbpedia.org/page/Day
A measure of time defined as 86 400 seconds.
https://doi.org/10.1351/goldbook.D01527
Day
http://qudt.org/vocab/unit/MPERSEC
SI coherent measurement unit for speed.
http://www.ontologyofunitsofmeasure.org/resource/om2/metrePerSecondTime
MetrePerSecond
The centimetre–gram–second (CGS) system of units.
https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units
CGS is a variant of the metric system.
CGSUnit
NonSI units mentioned in the SI.
https://en.wikipedia.org/wiki/NonSI_units_mentioned_in_the_SI
This is a list of units that are not defined as part of the International System of Units (SI), but are otherwise mentioned in the SI brouchure, because either the General Conference on Weights and Measures (CGPM) accepts their use as being multiples or submultiples of SIunits, they have important contemporary application worldwide, or are otherwise commonly encountered worldwide.
SIAcceptedSpecialUnit
″
http://qudt.org/vocab/unit/ARCSEC
Measure of plane angle defined as 1/3600 or a degree.
SecondOfArc
ArcSecond
B
http://qudt.org/vocab/unit/B
One bel is defined as `1⁄2 ln(10) neper`.
Unit of measurement for quantities of type level or level difference.
https://en.wikipedia.org/wiki/Decibel
Today decibel (one tenth of a bel) is commonly used instead of bel.
bel is used to express the ratio of one value of a power or field quantity to another, on a logarithmic scale, the logarithmic quantity being called the power level or field level, respectively.
Bel
Unit for quantities of dimension one that are the fraction of two areas.
Unit for solid angle.
AreaFractionUnit
Unit for quantities of dimension one that are the fraction of two volumes.
Unit for volume fraction.
VolumeFractionUnit
http://qudt.org/vocab/unit/M3
SI coherent measurement unit for volume.
http://www.ontologyofunitsofmeasure.org/resource/om2/cubicMetre
CubicMetre
l
http://qudt.org/vocab/unit/L
A nonSI unit of volume defined as 1 cubic decimetre (dm3),
https://doi.org/10.1351/goldbook.L03594
Litre
http://qudt.org/vocab/unit/M2
SI coherent measurement unit for area.
http://www.ontologyofunitsofmeasure.org/resource/om2/squareMetre
SquareMetre
Np
http://qudt.org/vocab/unit/NP
http://dbpedia.org/page/Neper
Unit of measurement for quantities of type level or level difference, which are defined as the natural logarithm of the ratio of power or fieldtype quantities.
The value of a ratio in nepers is given by `ln(x1/x2)` where `x1` and `x2` are the values of interest (amplitudes), and ln is the natural logarithm. When the values are quadratic in the amplitude (e.g. power), they are first linearised by taking the square root before the logarithm is taken, or equivalently the result is halved.
Wikipedia
https://en.wikipedia.org/wiki/Neper
https://doi.org/10.1351/goldbook.N04106
Neper
°
http://qudt.org/vocab/unit/DEG
http://dbpedia.org/page/Degree_(angle)
Degree is a measurement of plane angle, defined by representing a full rotation as 360 degrees.
https://doi.org/10.1351/goldbook.D01560
Degree
http://qudt.org/vocab/unit/NM
SI coherent measurement unit for torque.
http://www.ontologyofunitsofmeasure.org/resource/om2/newtonMetre
Note that the physical dimension is the same as for Joule.
NewtonMetre
Unit for fractions of quantities of the same kind, to aid the understanding of the quantity being expressed.
Quantities that are ratios of quantities of the same kind (for example length ratios and amount fractions) have the option of being expressed with units (m/m, mol/mol to aid the understanding of the quantity being expressed and also allow the use of SI prefixes, if this
is desirable (μm/m, nmol/mol).
 SI Brochure
FractionUnit
min
http://qudt.org/vocab/unit/MIN
http://dbpedia.org/page/Minute
NonSI time unit defined as 60 seconds.
Minute
Unit for quantities of dimension one that are the fraction of two lengths.
Unit for plane angle.
LengthFractionUnit
ha
http://qudt.org/vocab/unit/HA
http://dbpedia.org/page/Hectare
A nonSI metric unit of area defined as the square with 100metre sides.
https://en.wikipedia.org/wiki/Hectare
Hectare
eV
http://qudt.org/vocab/unit/EV
http://dbpedia.org/page/Electronvolt
The amount of energy gained (or lost) by the charge of a single electron moving across an electric potential difference of one volt.
https://doi.org/10.1351/goldbook.E02014
ElectronVolt
Unit for quantities of dimension one that are the fraction of two speeds.
Unit for refractive index.
SpeedFractionUnit
Measurement unit for electric dipole moment.
CoulombMetre
Unit for quantities of dimension one that are the fraction of two amount of substance.
Unit for amount fraction.
AmountFractionUnit
t
http://qudt.org/vocab/unit/TON_M
A nonSI unit defined as 1000 kg.
https://en.wikipedia.org/wiki/Tonne
https://doi.org/10.1351/goldbook.T06394
Tonne
g
http://qudt.org/vocab/unit/GM
Gram is defined as one thousandth of the SI unit kilogram.
https://en.wikipedia.org/wiki/Gram
https://doi.org/10.1351/goldbook.G02680
Gram
The class of individuals that stand for real world objects according to a specific representational perspective.
This class is the practical implementation of the EMMO pluralistic approach for which the only objective categorization is provided by the Universe individual and all the Quantum individuals.
Between these two extremes, there are several subjective ways to categorize real world objects, each one provide under a 'Perspective' subclass.
Perspective
The class of all individuals that stand for a real world not selfconnected object.
A 'Collection' individual stands for a nonselfconnected 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 selfconnected object which can be represented as a whole made of connected parts (e.g. a car made of components).
Formally, 'Collection' is axiomatized as the class of individuals that hasMember some 'Item'.
A 'Collection' cannot have as member another 'Collection'.
From Latin collectio, from colligere ‘gather together’.
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 nonconnected objects and not as a mereotopological selfconnected fusion.
Collection
The class of 'EMMO' individuals that stand for real world objects that can't be further divided in time nor in space.
For a physics based ontology the 'Quantum' can stand for the smallest identifiable portion of spacetime defined by the Planck limit in length (1.616e35 m) and time (5.39e44 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.
A 'Quantum' is the most fundamental subclass of 'Item', since its individuals stand for the smallest possible selfconnected 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.
A 'Quantum' stands for a 4D real world object.
A quantum is the EMMO mereological 4D atomic entity.
To avoid confusion with the concept of atom coming from physics, we will use the expression quantum mereology, instead of atomistic mereology.
From Latin quantum (plural quanta) "as much as, so much as;", introduced in physics directly from Latin by Max Planck, 1900.
Quantum
The class representing the collection of all the individuals declared in this ontology standing for real world objects.
'EMMO' is the disjoint union of 'Item' and 'Collection' (covering axiom).
The union implies that 'EMMO' individuals can only be 'Item' individuals (standing for selfconnected 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 selfconnected and nonself connected at the same time.
For the EMMO ontologist the whole universe is represented as a 4D pathconnected topological manifold (i.e. the spacetime).
A real world object is then a 4D topological subregion of the universe.
A universe subregion is isolated and defined as a real world object by the ontologist. Then, through a semiotic process that occurs at metaontological 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 selfconnectedness: a real world object can be selfconnected xor not selfconnected.
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.
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.
EMMO
A real world object is selfconnected 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 pathconnectivity concept we can define a selfconnected real world object as an object for which each couple of points is pathconnected.
An 'Item' individual stands for a real world selfconnected 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.
From Latin item, "likewise, just so, moreover".
Item
The basic constituent of 'item's that can be proper partitioned only in time up to quantum level.
According to mereology, this should be call 'atomistic' in the strict etimological sense of the word (from greek, atomos: undivisible).
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.
From Latin elementārius (“elementary”), from elementum (“one of the four elements of antiquity; fundamentals”)
While a 'Quantum' is atomistic in time and space, an 'elementary' is atomistic only in space, recalling the concept of elementary particle.
Elementary
A 'Item' that has no 'Physical' parts.
From Latin vacuus, “empty”.
The void concept is paramount for the representation of physical systems according to quantum theory.
Void
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).
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).
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 subcomponents (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.
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.
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.
In the EMMO there are no relations such as occupiesSpace, since 'Physical's are themselves the 4D regions.
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 nonlocality 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 subparts 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 subpart 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 subparts 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 subpart observables is interpreted as wavefunction collapse and leads to the end of the whole and the declaration of the subparts 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 BornOppenheimer approximation the user represent the atom by unentangling nucleus and electronic cloud. The unentanglement 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 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. NavierStokes or Euler equation applied to the same fluid are an example of mathematical model used to represent a physical object for some specific interpreter.
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European Materials & 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.
EMMO is released under a Creative Commons license Attribution 4.0 International (CC BY 4.0).
Access, DE
Fraunhofer IWM, DE
Goldbeck Consulting Ltd (UK)
SINTEF, NO
University of Bologna, IT
Adham Hashibon
Emanuele Ghedini
Georg Schmitz
Gerhard Goldbeck
Jesper Friis
https://creativecommons.org/licenses/by/4.0/legalcode
EMMC ASBL
European Materials & Modelling Ontology
Contacts:
Gerhard Goldbeck
Goldbeck Consulting Ltd (UK)
email: gerhard@goldbeckconsulting.com
Emanuele Ghedini
University of Bologna (IT)
email: emanuele.ghedini@unibo.it
The EMMO requires FacT++ reasoner plugin in order to visualize all inferences and class hierarchy (ctrl+R hotkey in Protege).
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