Mereocausality
The EMMO represents the world merging two fundamental approaches: mereology and causality. Mereology is about the relations between a whole and its parts, while causality is about ordering entities according to causal principles. The union of both theories into a single one, for the representation of our physical universe is called mereocausality, a discipline that has been defined by the EMMO developers.
The full theory beyond EMMO mereocausality [1] is quite intricate and rooted on some quantum field theory basic concepts. However, it can be used to define several useful terms and relations that we use every day using our language to express our experience of the world, and that can be used intuitively by any user.
In this tutorial we will understand how to use them, step by step. But remember, not matter how easy it seems, behind each term or relation there is a logical path provide by the full EMMO theory that roots them down to the level of elementary particle and forces, that is completely hidden by end users but available by more advanced users that wants to dig into it.
[1] F.A. Zaccarini, C. Masolo, E. Ghedini, S. Borgo, From Causation (and Parthood) to Time: The Case of EMMO, Frontiers in Artificial Intelligence and Applications 377 (2023), p. 92-106, https://doi.org/10.3233/FAIA231120
While a theory about parts may give you the impression of being trivial, after few steps into it we can assure that it is absolutely not the case. Mereology is a quite well developed logical theory^fn2 that provides some powerful conceptual tools to represent the world. Here we will introduce mereological concepts in a very simple and intuitive way using the EMMO relation hierarchy, showing how you can use them in the EMMO to express relations between entities.
The basic relation that we introduce is overlapping, and represent the concept of entities having a part in common. In the EMMO we use :overlaps to state overlapping and :notOverlaps to state non-overlapping between two entities.
Referring to the figure showing three entities :a, :b and :c
we can state that :a :overlaps :b and :a notOverlaps :c. It is evident that overlapping and non-overlapping are symmetric, since :b :overlaps :a and :c :notOverlaps :a. But while overlap is reflexive, since and entity is always overlapping itself :a :overlaps :a , non-overlapping is irreflexive, since an entity never overlaps itself.
The following figure shows all possible cases expressed by :a :overlaps :b
Now, let's start to distinguish between the above overlapping cases introducing the parthood relation, expressed by :hasPart that describes when an entity is completely contained into another. It is clear that in both cases
a is in relation with b with the expression :a :hasPart :b . The parthood relation characteristics are:
- reflexive, since an entity has part itself
-
antisymmetric, since when
:a :hasPart :band:b :hasPart :aas in the first case then:ais the same as:b -
transitive, since if
:a :hasPart :band:b :hasPart :c, then:a :hasPart :c
The first case can be expressed by :a :equalsTo :b, where with :equalsTo we express equality. While the second case is expressed by a proper parthood relation :hasProperPart, where :a :hasPart :b but not viceversa.
The inverse relation of :hasPart is :isPartOf and shares the same characteristics, but goes from :b to :a.
What about the remaining two overlapping cases? It seems that in both cases :a is always covered totally or partially by :b, without equality. This concept is capture by overcrossing, expressed by :isOvercrossedBy.
Both cases are described by :a :isOvercrossedBy :b. The characteristic of:isOvercrossedBy is to be irreflexive, in order to avoid equality.
The first case can easily expressed univocally by proper parthood as :a :isProperPartOf :b, using the inverse relation of :hasProperPart. The second one by a proper overlap relation :a :properOverlaps :b expressing overlap without equality, that is symmetric.
All the aforementioned relations, and their characteristics, are summarised in the following two hierarchies that constitute the upper part of the EMMO relations, one for the direct and one for the inverse relations.
These relations alone already provide a very powerful toolkit for the representation of state of things in the world, and are the mereological backbone of the EMMO.
The most simple examples for mereology applications is about objects and their composition, in a 3D interpretation of entities. For example, a car can be decomposed up to its fundamental constituents in a mereological chain of proper part relations.
:car :hasProperPart :wheel, :engine .
:engine :hasProperPart :piston .
:piston :hasproperPart :metallic_material .
:metallic_material :hasProperPart :grain .
:grain :hasProperPart :crystal_cell .
:crystal_cell :hasProperPart :atom .In this example we shift towards a 4D interpretation of entities, that is somewhat implicit in our language expressions. For example, to express that we knew someone we sometimes say that "our lives crossed", considering our lifetime as 4D entity extending both in space and time. Similarly, to express that we participate to an event we say that we "take part", meaning that we are one of the part of the event, the overlapping part between our lifetime and the event.
Let's make the example of an athlete and Olympic games. We can state that Tokyo and Rome marathons have been part of their respective Olympic games activities. Abebe Bikila took part in both marathons, meaning that his life overlapped the two events. This can be expressed as:
:TokyoMarathon :isProperPartOf :Olympics1964 .
:RomeMarathon :isProperPartOf :Olympics1960 .
:AbebeBikila :properOverlaps :TokyoMarathon, :RomeMarathon .
From the previous statement it is possible to infer the participation of Bikila to both Olympics games:
:AbebeBikila :properOverlaps :Olympics1960, :Olympics1964 .
Finally, an important feature of the EMMO is the commitment to the existence of a fundamental 'a-tomic' (etymologically: in-divisibile) level for parts. This is expressed by defining the class of the entities that have no proper parts, that in the EMMO is called :Quantum, to avoid misunderstandings with the chemical concept of atom, and the assertion that every entity has at least a quantum part.
What is the interpretation of :Quantum? It may be interpreted as an elementary particle between two fundamental forces interactions, but we need to wait the definition of causality to fully understand it.
The EMMO is not a spacetime-based but a causality-based ontology. The motivation is that if you want to develop an ontology for physics you have to seriously take into account relativity and quantum mechanics, and causality is a relation between events that is invariant for special and general relativity (we will take care later of quantum mechanics). So, every causal statement expressed by the EMMO is valid for every observer.