Part-to-whole ratio in temporal / event ontology

The initial publication of the cycle (“ Classes, sets, groups, systems ”) concluded that the traditional classification of individuals by attributing them to certain classes-sets cannot be considered homogeneous, and one should distinguish (1) the inclusion of individuals as parts in a complex object ( integer) and (2) the fall of individuals under concepts that can be divided into conceptual and relational . In the second text (“ Conceptual description of individuals ”) the original hierarchy of conceptual concepts was proposed (“category - type - concept - genus - type - species - individual”). In the current publication we will discuss the classification of relations such as "part – whole". In linguistic thesauruses and in ontologies of the upper level (WordNet, RuTez, SUMO, CYC Ontology, DOLCE), various options for distinguishing the subspecies of the "part - whole" relationship are described. The text proposes another way of classification.

In everyday language, we often use the term “part” to indicate that an object belongs to another object belongs to it. The following is a list of typical statements about the belonging of a certain entity as part of another entity, understood as a whole :

1. The wheel is part of the car.
2. The heart is part of the circulatory system.
3. The hand is part of man.
4. The top is part of the tree.
5. The tree is part of the forest.
6. The ship is part of the fleet.
7. The painting is part of the collection.
8. The contents of this bag are only part of what I bought.
9. The person is part of a trade union.
10. The goalkeeper is part of the football team.
11. The head is part of the novel.
12. The act is part of the play.
13. Spring is part of the year.
14. Goalkeeper area is part of the football field.
15. Pskov region - part of Russia.
16. Moscow is a part of Russia.
17. Thermodynamics is part of physics.
18. A slice of bread is part of a loaf.
19. Gin is part of martini.
20. A portion of water is part of the water in the glass.
21. Carbon is part of methane.

Even with a cursory review of this list, it can be noted that not all situations in which we state that something is a part of something else have the same ontological meaning, that is, they can be described in the same type when creating models of subject areas. In some cases, parts (for example, wood, wheel) have independent certainty and outside the whole (forest, car) and can be moved from the whole to the composition of the other (the wheel can be put on another machine, the tree can be transplanted into the next forest). While other parts (treetop, thermodynamics, goalkeeper’s playground) are immanent fragments of the whole, do not have independent existence outside of it (thermodynamics, whatever one may say, will always be part of physics, and the goalkeeper's playground outside the football field is just a rectangular segment). There is a whole that ceases to be what it is when some of its parts are removed: the heart from the circulatory system, the wheel from the car, the atom from the methane molecule. Others are indifferent to changing their composition: trees in the forest can be cut down or planted new, and the forest will remain a forest (of course, to a certain extent), the dismissal of even the trade union president will not affect the existence of the organization. That is, it turns out that the word “part” in the above phrases is used in several meanings:

1. detail, functional element of the system (wheel, heart),
2. a fragment of a thing (the top of a tree, the hand of a man),
3. fragment of spatial or temporal essence (act of the performance, goalkeeper’s platform, spring),
4. element of the set (tree in the forest, ship of the fleet, union member),
5. subset of the set (part of the purchased products),
6. blend component (gin in martini),
7. a portion, a piece obtained by separating something (a slice of bread, a portion of water in a glass),
8. falling under the concept, an element of classification (thermodynamics is part of physics).

A certain complexity is also caused by the fact that the same statement about the belonging of a part to the whole can be interpreted in different ways: for example, the judgment “Moscow is part of Russia” can have meaning and “the territory of Moscow is a fragment of the territory of Russia”, and “Moscow is an element in many cities of Russia ”, or the phrase“ the arm is a part of a man ”may also indicate a fragment of the human body (for example, when describing the rules of the game of football) and an element / detail of the body's motor-support system (in physiology).
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Therefore, we have to make two obvious conclusions:

1. the same object, participating in different situations / events, can be considered as part of different integers, and
2. most importantly, when creating domain models, we should be able to formally fix the difference in the meanings of using the term “part”.

Classification of relations "part - whole"

By combining some items from the list of meanings of the term “part”, we can offer the following variant of distinguishing the specific relations “part-whole”:

1. element / part - system
2. fragment / region - spatial or temporal essence,
3. member - many
4. the piece is the whole
5. component - a mixture.

The proposed classification is based on a temporal / eventual ontology (see “ Subject-event approach to modeling complex systems ”), offering to consider events as the initial ontological entity — in this case, events with which the whole is fixed (formed or changed); parts, relationships are established between the individual parts and between the part and the whole:

1. element - system : assembly / disassembly, element replacement, fixation of functional and causal relations between elements and elements and the system;
2. fragment - essence : selection, restriction, fixation of positional relations between fragments (border, further / closer, earlier / later) and fragments and the whole (center / periphery, start / end);
3. member - set : membership fixation, inclusion / exclusion (there is no relationship between the elements);
4. a piece is an integer : divide, break, cut off (there are no relations between the elements);
5. component - mixture : mix, combine (the relationship between the elements are absent).

In some subject areas, as a kind of member-set relationship, it is possible to distinguish a member-collection relationship, which serves to describe ordered sets of ontologically distinct, heterogeneous objects.

Temporal relationship "part-whole"

It should be particularly noted that the relationship “piece - whole” and “component – ​​mixture” is generally problematic to be counted as “part – whole”, since in them the parts and the whole do not exist simultaneously. So, when fixing the “piece-whole” relationship, before separating the piece, there is no whole part — we have a homogeneous whole object (water in a glass, a loaf of bread), and after the piece is removed, this object (the whole) disappears (we have two portions of water and two pieces of bread, and there is no longer the original glass of water and a loaf). And it is clear that, unlike the “member-set” and “fragment-essence” relations, the “piece-whole” relationship can be adequately described only in a temporal ontology, in which the event of separation of a piece from the whole, after which the object-whole disappears, can be fixed. .

A similar problem arises in the ontological interpretation of the statement “gin is part of martini,” which, obviously, should be described by the “component-mixture” relationship. It is clear that if we put a martini glass in front of us, then in it, or rather, in the liquid in the glass, it is impossible to indicate such a part as “gin”. A part is something singled out, represented as an independent object, which, of course, are the details of the systems, the members of the sets, fragments and pieces. In mixtures, alloys, solutions such parts are indistinguishable. Moreover, it is difficult to imagine such ontological situations, events in which it would be necessary to isolate a part of the “gin” from an already prepared martini. It is possible to point to the constituent parts of martini - gin and vermouth - only before the whole appears. Consequently, here, as in the case of the “piece-whole” relationship, we are dealing with a situation where the parts and the whole do not exist simultaneously: the originally existing parts disappear forming a new whole. It is clear that the relationship “component - mixture” is advisable to enter only for the subject area, in which the event of formation of the whole of the parts is fixed, say, when describing the martini preparation procedure, which, of course, requires a temporal ontology. If we are talking only about the description of actions with the mixture itself, that is, using the drink, then it would be more correct to introduce an additional “recipe” object and describe it as a collection of the concepts of “gin” and “vermouth”.

Temporal ontology is also necessary for a full description of the “element-system” relationships, firstly, because systems can be dynamic, and, secondly, an event of removing an element can turn a system into a multitude, for example, a car into a collection of parts.

The transitivity of the "part - whole" relationship

Transitivity - parts of parts are parts of the whole - is the most important of the three axioms (plus reflexivity and antisymmetry) for the "part-whole" relationship. In the proposed classification, as in some other variants of classifications, transitivity is performed only within certain types of relationships: a detail is a part of the system (the rim is a detail of the wheel, and therefore the detail of the machine), a fragment of the fragment is a fragment of the whole entity (wrist is a fragment hands and a fragment of a person, the scene of an act is a fragment of a performance), a member of a subset is a member of a set (a member of a regional trade union is also a member of the All-Russian trade union), a piece of a piece is a piece of initially divided by a whole, the component component is a component of the mixture. In this way, the problem of transitivity is fundamentally resolved, arising from a generalized understanding of the “part-whole” relationship, which is usually demonstrated by example: a person is a part of a trade union, an arm is a part of a man, therefore the hand is part of a trade union. In the proposed classification, the situation changes radically: a person is a member of the “trade union” set, and a hand is a fragment of a person, therefore, it can not be considered as a member of a set, or, for example, a bolt is a machine part, a thread is a fragment of a bolt, which means , the thread is not part of the machine, or the machine is a member of the collection, but the wheel as part of the machine is no longer included in the collection. A special note should be made about transitivity in the relationship “fragment - essence” - it persists only when fragments are singled out on the same basis: either spatial or temporal (it is clear that a person’s youth’s temporal fragment cannot correlate with its spatial separation). fragment "belly").

Examples and Explanations

A car in the workshop subject area, of course, must be described as a system of elements / parts, while a temporal / event ontology must be used to record events of replacement parts. To describe the functioning of the car wash, the car should be presented as a whole with fragments: bumper, body, wheels - it’s clear that in this case we are not in the details of the system, but in the wash zones. In a garage, a car is a member of a collection, and for a traffic management system it is a member of a set. In the ontology of a landfill, a car must be described as a whole, cut into pieces.

The statement “goalkeeper is part of a football team” can be interpreted as a statement of the “element-system” relationship if it is about the structure of the football team (goalkeeper, defenders, attackers), and as “member-collection” if the specific goalkeeper is meant (Ivanova) to the list of the team.

The statement “carbon is part of methane” indicates the element-system relationship when it comes to the composition of the methane atom, which contains the carbon atom as an element, or the component-mixture ratio when describing methane synthesis (hypothetically, because methane not derived from pure carbon).

Conclusion

The statement that something is considered as part of something else is not ontologically homogeneous and, taking into account variants of temporal, spatial and functional connections of parts and the whole, can indicate the following types of relationships: “element / detail - system”, “fragment / region - spatial or temporal the essence, the member is the set (as a variant the member is the collection), the piece is the whole and the component is the mixture. Transitivity is preserved only within the above relations. For the exact definition of relationships and the establishment of formal links between parts and the whole, additional research is required.

Literature

1. Lukashevich N. Part-to-whole relations: theory and practice // Neurocomputers: development, application. - 2013. - № 1. - p. 7–12.
2. J. Odell “Six different kinds of composition” Journal of Object-Oriented Programming, (January 1994)
3. Varzi, A., “Mereology”, in EN Zalta (ed.), The Stanford Encyclopedia of Philosophy, 2014. http://plato.stanford.edu/entries/mereology