Mereocausality
The EMMO is designed to represent actual world entities that are physically interactable. To do so, it makes usage of the concepts of:
- parthood, to represent how parts and wholes entities are related (substituting set theory), moving from the fundamental entities up to the universe
- causality, to represent how entities are related between each other, interpreting causality between two entities as the existence of a fundamental physical interaction between their parts.
The mereocausal level can be considered the EMMO onto-logical section, since mereocausality relations and classes express the fundamental properties of bare beings (ὄντα). No temporal or spatial frame is required. Caused and affected entities are the outcomes of this representation that possess some similarities with temporal orderings.
While this approach, despite the fact that may seem a bit abstract, constitutes a really powerful and flexible foundation to embrace all concepts (classes and relations) that will be used on much more specific ontology modules.
The EMMO is based on the primitive concepts of atomism and causality:
- Atomism is about the fact that every world entity is the sum of several fundamental entities that we call quantum (to avoid them being confused with the widely used concept of atom in physics and chemistry). A quantum can be thought as an elementary particle between two interactions (e.g. an electron between two scattering events). We use the relation of parthood to express that a macro-entity (a composite world entity) is made of some specific quantums, or of some intermediate macro-entities. Given this terminology we can state that a quantum possesses no parts.
- Causality is about the fact that the relation between macro-entities are governed by causality relations between their quantum constituents. In this picture, quantum entities are connected through a network of causal relations that describes the connections between macro-entities.
The combination of atomism and quantum-based causality defines the EMMO as a strong reductionistic-based ontology, enabling a multi-granular and multi-scale representation of world entities.
It is important to underline that quantums are neither in space nor time. Spatial and temporal relations between quantums and between macro-entities emerge according to the underlying causality network that connects them. Due to this approach, the EMMO can be considered a 4D ontology, since all entities larger than quantums are always extended in time, due to the nature of elementary particle interactions.
The name mereocausality comes from the combination of mereology, the science describing the relations between wholes and parts, and causality that are declared in the mereocausality module.
The expressivity of OWL 2 DL doesn't allow to fully implement the rigorous mereocausality theory developed in the First Order Logic (FOL) version of the EMMO. Instead, the EMMO OWL 2 DL will be based a generic causality relation that holds for both quantum and macro entities and a weaker mereology theory, using primitive concepts to define what in EMMO FOL would instead be rigorously derived from first principles.
There are two types of EMMO relations in the mereocausality module: the mereological and the causal relations.
The mereological relations describes the relations occurring between parts and wholes. The most general mereological concept is overlapping, expressed by the Object Relation :isOverlapping (reflexive, symmetric) that applies between two entities intersecting each other. Together with its negation :isNotOverlapping, they provide a covering for all entities, meaning that every two entities :x and :y are either in an overlapping or in a non-overlapping relation.
An overlap is a parthood when there is a total overlap of one entity on the other, or an overcrossing when there is a partial overlap. These two concepts are formalised by the :isOvercrossing (irreflexive, symmetric) and :hasPart (reflexive, anti-symmetric, transitive) relations.
A part is called proper part when there is a part of the whole that is not overlapped by it. If two entities :x and :y completely overlaps each other, then they are the same entity. Proper parthood is expressed by the :hasProperPart (irreflexive, asymmetric, transitive) relation. The relation of parthood for two completely overlapping entities is :hasIdenticalPart and relates two entities that are in fact a single one (meaning that the symbol :x and :y are simply two names for the same thing, i.e. they refer to the same world entity).
An atomistic entity in mereology is defined as an entity that possesses no proper parts. In the EMMO it is called a quantum, defined in OWL as the :Quantum class, and is represented by a filled black dot.
Mereological atomism requires that any world entity is in the end made of quantums. A mereological sum of quantums is a macro-entity and is generally represented as a box, whose parts (quantums or other macro-entities) may or may not be depicted depending on the context.
A quantum is a special case of macro-entity.
Mereological relations are summarised in the following tree:
The cause relation describes the causal dependency of an entity with respect to the others and is expressed by the ObjectProperty :isCauseOf (irreflexive). The negation of :isCauseOf that is formalized as :isNotCauseOf so that every two entities are either in causal or in non-causal relation.
The :isCauseOf relation can be used to express causality between quantum entities.
This relation can also be applied to macro-entities: for any two macro-entities x and :y, the axiom :x :isCauseOf :y is valid if and only if there exist at least two quantums :qx and :y, with :x :hasPart qx and :y :hasPart :qy, for which holds :qx :isCauseOf :qy.
Furthermore, two entities in :isCauseOf relations are required not to overlap (always true for quantums), so that :x :isCauseOf :y implies :x :isNotOverlapping :y .
The EMMO FOL defines a more fundamental causality relation that occurs between quantum entities only, being irreflexive, asymmetric and transitive, and establishing a strict partial order. This more fundamental relation can describe the interactions occurring at elementary particle level, implementing de facto a multi-scale representation of world entities up to elementary particle level. However, the limitations of OWL 2 DL language suggest to limit the EMMO OWL theory to a more general causality relation :isCauseOf that is tailored to deal mainly with causality between macro-entities.
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