Important concepts
Important concepts¶
Mereotopological composition¶
Substrate¶
A substrate represents the place (in general sense) in which every real world item exists.
It provides the dimensions of existence for real world entities.
This follows from the fact that everything that exists is placed somewhere in space and time.
Hence, its space and time coordinates can be used to identify it.
Substrates are always topologically connected spaces. A topological space, X, is said to be disconnected if it is the union of two disjoint non-empty open sets. Otherwise, X is said to be connected.
substrate is the superclass of space, time and their combinations, like spacetime.
Following Kant, space and time are a priori forms of intuition, i.e. they are the substrate upon which we place our intuitions, assigning space and time coordinates to them.
Hybrid¶
A hybrid is the combination of space and time.
It has the subclasses world_line (0D space + 1D time), world_sheet (1D space + 1D time), world_volume (2D space + 1D time) and spacetime (3D space + 1D time).
Spacetime¶
EMMO represents real world entities as subclasses of spacetime.
A spacetime is valid for all reference systems (as required by the theory of relativity).
Matter¶
matter is used to represent a group of elementary in an enclosing spacetime.
As illustrated in the figure, a matter is an elementary or a composition of other matter and vacuum.
In EMMO matter is always a 4D spacetime.
This is a fundamental difference between EMMO and most other ontologies.
In order to describe the real world, we must also take into account the vacuum between the elementaries that composes higher granularity level entity (e.g. an atom).
In EMMO vacuum is defined as a spacetime that has no elementary parts.
Existent¶
An existent is defined as a matter that unfolds in time as a succession of states.
It is used to represent the whole life of a complex but structured state-changing matter entity, like e.g. an atom that becomes ionised and then recombines with an electron.
On the contrary, a matter and not existent entity is something "amorphous", randomly collected and not classifiable by common terms or definitions.
That is a heterogeneous heap of elementary, appearing and disappearing in time.
State¶
A state is matter in a particular configurational state.
It is defined as having spatial direct parts that persist (do not change) throughout the lifetime of the state.
Hence, a state is like a snapshot of a physical in a finite time interval.
The use of spatial direct parthood in the definition of state means that a state cannot overlap in space with another state.
An important feature of states, that follows from the fact that they are spacetime, is that they constitute a finite time interval.
Elementary¶
The basic assumption of decomposition in EMMO, is that the most basic manifestation of matter is represented by a subclass of spacetime called elementary.
The elementary class defines the "atomic" (undividable) level in EMMO.
A generic matter can always be decomposed in proper parts down to the elementary level using proper parthood.
An elementary can still be decomposed in temporal parts, that are themselves elementary.
Example of elementaries are electrons, photons and quarks.
Granularity - direct parthood¶
Granularity is a central concept of EMMO, which allows the user to percieve the world at different levels of detail (granularity) that follow physics and materials science perspectives.
Every material in EMMO is placed on a granularity level and the ontology gives information about the direct upper and direct lower level classes.
This is done with the non-transitive is_direct_part_of relation.
Granularity is a defined class and is useful sine a reasoner automatically can put the individuals defined by the user under a generic class that clearly expresses the types of its compositional parts.
Mathematical entities¶
The class mathematical_entity represents fundamental elements of mathematical expressions, like numbers, variables, unknowns and equations.
Mathematical entities are pure mathematical and have no physical unit.
Natural law¶
A natural_law is an abstraction for a series of experiments that tries to define a common cause and effect of the time evolution of a set of interacting participants.
It is (by definition) a pre-mathematical entity.
The natural_law class is defined as
is_abstraction_for some experiment
It can be represented e.g. as a thought in the mind of the experimentalist, a sketch and textual description in a book of science.
physical_law and material_law are, according to the RoMM and CWA, the laws behind physical equations and material relations, respectively.
Properties¶
Properties are abstracts that are related to a specific material entity with the relation has_property, but that depend on a specific observation process, participated by a specific observer, who catch the physical entity behaviour that is abstracted as a property.
Properties enable us to connect a measured property to the measurement process and the measurement instrument.