boldachev February 10, 2016 at 16:13

Part-whole relationship in temporal / event ontology

The original publication of the cycle (“ Classes, Sets, Groups, Systems ”) ended with the conclusion that the traditional classification of individuals by assigning them to one or another set of classes cannot be considered homogeneous, and one should distinguish (1) the inclusion of individuals as parts in a complex object ( the whole) and (2) the inclusion of individuals under concepts that can be divided into conceptual and relational . In the second text (“ Conceptual description of individuals") An original hierarchy of conceptual concepts was proposed (" category - type - concept - gender - species - variety - individual "). In the current publication, we will focus on the classification of “part-whole” relationships. In linguistic thesauruses and in ontologies of the upper level (WordNet, RuTez, SUMO, CYC Ontology, DOLCE), various options for distinguishing subspecies of the part-whole relationship are described. The text proposes another classification method.

In common language, we often use the term "part" to indicate that an object is part of 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 :

The wheel is part of the car.
The heart is part of the circulatory system.
The hand is part of man.
The top is part of a tree.
The tree is part of the forest.
The ship is part of the fleet.
The painting is part of the collection.
The contents of this bag are only part of what I bought.
A person is part of a trade union.
Goalkeeper is part of a football team.
The chapter is part of the novel.
The act is part of the play.
Spring is part of the year.
Goalkeeper area is part of the football field.
Pskov region is part of Russia.
Moscow is part of Russia.
Thermodynamics is part of physics.
A slice of bread is part of a loaf.
Gin is part of a martini.
A portion of water is part of the water in the glass.
Carbon is part of methane.

Even a quick look at this list, you will notice that not all situations in which we state that something is part of another something, have the same ontological meaning, that is, they can be described in the same way when compiling domain models. In some cases, parts (for example, a tree, a wheel) have independent certainty even outside the whole (forest, car) and can be moved from this whole to another (the wheel can be put on another car, the tree can be transplanted into a neighboring forest). While other parts (the top of the tree, thermodynamics, goalkeeper area) are immanent fragments of the whole that do not have an independent existence outside it (thermodynamics, anyway, will always be part of physics, and the goalkeeper area outside the football field is just a rectangular area). There is a whole that ceases to be what it is when you remove some of its parts: the heart from the circulatory system, the wheels from the car, an atom from a methane molecule. Other integers are indifferent to changes in their composition: trees in the forest can be cut down or new trees planted, and the forest will remain a forest (to a certain extent, of course), dismissal of even the union chairman 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:

detail, functional element of the system (wheel, heart),
a fragment of a thing (top of a tree, a person’s hand),
a fragment of a spatial or temporal essence (act of a performance, goalie area, spring),
element of the multitude (tree in the forest, fleet ship, union member),
a subset of the set (part of the purchased products),
component of the mixture (gin in martini),
portion, piece obtained by dividing something (a slice of bread, a portion of water in a glass),
falling under the concept, element of classification (thermodynamics is part of physics).

A certain difficulty is 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 proposition “Moscow is part of Russia” can also mean “Moscow territory is a fragment of Russian territory” and “Moscow is an element in many cities of Russia ”, or the phrase“ the hand is part of a person ”can indicate both a fragment of the human body (say, when describing the rules of the game of football) and an element / detail of the motor-supporting system of the body (in physiology).

Therefore, we must draw two obvious conclusions:

one and the same object, participating in different situations / events, can be considered as part of various whole, and
most importantly, when creating models of subject areas, we should be able to formally record the difference in the values of the use of 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 option for distinguishing specific relations "part - whole":

element / part - system,
fragment / region - spatial or temporal entity,
member is a multitude
a piece is a whole
component is a mixture.

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

element - system : assembly / disassembly, element replacement, fixing functional-causal relations between elements and elements and the system;
fragment - essence : selection, restriction, fixing of positional relations between fragments (border, further / closer, earlier / later) and fragments and the whole (center / periphery, beginning / end);
member - many : fixation of belonging, inclusion / exclusion (there are no relations between elements);
a piece is a whole : split, break, cut off (there are no relations between the elements);
component - mixture : mix, combine (there are no relations between the elements).

In some subject areas, as a variety of the “member – set” relationship, it is possible to distinguish the “member – collection” relationship, which serves to describe ordered sets of ontologically distinguishable, heterogeneous objects.

Temporality of the part-whole relationship

Particular attention should be paid to the fact that the relations “piece - whole” and “component - mixture” are generally problematic to be classified as “part - whole”, because in them parts and the whole do not exist simultaneously. So, when fixing the “piece - whole” relationship until the piece is separated, the whole does not have any parts - we have a homogeneous whole object (water in a glass, a loaf of bread), and after separating the piece this object (whole) disappears (we have two portions of water and two slices of bread, and there is no longer the original glass of water and a loaf). And it is clear that, in contrast to the relations “member - set” and “fragment - essence”, the relation “piece - whole” can be adequately described only in temporal ontology, in which one can record the event of separation of a piece from the whole, after which the object-whole disappears .

A similar problem arises in the ontological interpretation of the statement “gin is part of a martini”, which, obviously, should be described by the relation “component - mixture”. It is clear that if we set ourselves a glass of martini, 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 distinguished, presented as an independent object, which, of course, are the details of systems, members of 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. Pointing out the components of martini - gin and vermouth - is possible only before the whole appears. Hence here as in the case of the “piece - whole” relationship, we are dealing with a situation where parts and the whole do not exist simultaneously: the originally existing parts disappear to form a new whole. It is clear that the “component – mixture” relationship is expediently introduced only for the subject area in which the event of the formation of a whole of parts is recorded, say, when describing the martini preparation procedure, which, of course, requires a temporal ontology. If we are only talking about the description of the actions with the mixture itself, that is, the use of the drink, then it would be more correct to introduce an additional object “recipe” and describe it as a collection of concepts “gin” and “vermouth”. that it is advisable to introduce the “component – mixture” relationship only for the subject area in which the event of the formation of a whole of parts is recorded, say, in the description of the martini preparation procedure, which, of course, requires temporal ontology. If we are only talking about the description of the actions with the mixture itself, that is, the use of the drink, then it would be more correct to introduce an additional object “recipe” and describe it as a collection of concepts “gin” and “vermouth”. that it is advisable to introduce the “component – mixture” relationship only for the subject area in which the event of the formation of a whole of parts is recorded, say, in the description of the martini preparation procedure, which, of course, requires temporal ontology. If we are only talking about the description of the actions with the mixture itself, that is, the use of the drink, then it would be more correct to introduce an additional object “recipe” and describe it as a collection of concepts “gin” and “vermouth”.

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

The transitivity of the relationship "part - whole"

Transitivity - parts of parts are parts of the whole- is the most important of the three axioms (plus reflexivity and antisymmetry) for the relationship "part - whole." In the proposed classification, as in some other types of classifications, transitivity is performed only within certain types of relations: a part is a part of a system (a rim is a part of a wheel, and therefore a part of a machine), a fragment of a fragment is a fragment of a whole entity (wrist is a fragment hands and a fragment of a person, the scene of the act is a fragment of the play), a member of the subset is a member of the multitude (a member of the regional trade union is also a member of the All-Russian trade union), a piece of a piece is a piece of After a whole separation, the component of the component is the component of the mixture. In this way, the problem of transitivity, which arises with a generalized understanding of the relations “part-whole”, is fundamentally solved which is usually demonstrated by example: a person is part of a union, the hand is part of a person, hence the hand is part of a union. In the proposed classification, the situation changes radically: a person is a member of the “union” set, and a hand is a fragment of a person, therefore, it can not be considered as a member of the set, or, for example, a bolt is a machine part, a thread is a fragment of a bolt, which means , the thread is not a 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 remark should be made about the transitivity in the “fragment - essence” relationship - it is preserved only when the fragments are selected on one basis: either spatial or temporal (clearly,

Examples and explanations

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

The statement “goalkeeper is part of a football team” can be interpreted both as a statement of the “element – system” relationship when it comes to the structure of a football team (goalkeeper, defenders, forwards) and as “member - collection” if it refers to the identity of a specific goalkeeper (Ivanova) to the payroll.

The judgment “carbon is part of methane” indicates the “element – system” relationship when it comes to the composition of the methane atom, which includes the carbon atom as an element, or the “component – mixture” ratio when describing methane synthesis (hypothetically, since methane not obtained from pure carbon).

Conclusion

A statement that something is considered as part of another something is not ontologically homogeneous and, taking into account the options for temporal, spatial and functional relationships of parts and the whole, can indicate the following types of relations: “element / detail - system”, “fragment / region - spatial or temporal essence ”,“ member - set ”(as an option“ member - collection ”),“ piece - whole ”and“ component - mixture ”. Transitivity is preserved only within the listed relations. For the exact determination of relations and the establishment of formal relations of parts and the whole, additional research is required.

Literature

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

Tags: