Abs tract Cur rent ont ologi es' upp er-le vel tax onomi c str uctur e is oft en qui te com plica ted and har d to und ersta nd. In thi s pap er I sho w how the the oret ical too ls of so- calle d For mal Ont ology , and esp ecial ly the the ory of ide ntity , can hel p to for mulat e cle aner, mor e gen eral, mor e rig orous , and mor e und ersta ndabl e upp er-le vel ontol ogies . I foc us in par ticul ar on som e exa mple s of mul tiple gen erali zatio n, pro posin g a way of sim plify ing the dom ain str uctur e by spl ittin g som e con cepts acc ordin g to dif feren t ide ntity con ditio ns, or by exc ludin g the m becau se of the ir lim ited org aniza tiona l rol e.
http://www.ladseb.pd.cnr.it/infor/ontology/ontology.html
1. Introduction
Currently, a number of efforts in the area of knowledge
and language engineering are aimed to the development of
systems of basic semantic categories (often called
"upperlevel ontologies"), to be used for various applications
such as natural-language processing, multilingual
information retrieval, information integration, intelligent
systems design. Examples of such systems are CYC's upper
level, Penman's Upper Model
This paper intends to show how the theoretical tools of
so-called Formal Ontology
One of the problems with IS-A when considering linguistic ontologies like WordNet is that it often reflects a lexical relation between words, rather than an ontological relation between classes of domain entities. Although this fact is well known, the tendency to confuse the two aspects is quite high, especially when linguistic ontologies are used for non-linguistic applications. For instance, a common habit in linguistic ontologies is to rely on multiple inheritance for representing polysemy, as in the case of Figure 1. This results in an overloading of IS-A's role, which, as we shall see, may cause serious semantic problems.
To overcome these problems, the solution I propose is to pay more attention to the ontological implications of taxonomic choices, limiting IS-A links to connect nodes sharing a common identity criterion. In this way, the taxonomy reflects a basic ontological structure with a clear semantics, while the extra-information currently encoded by IS-A links can be represented by means of specialized links and attributes.
I will consider the following examples of IS-A links:
1. A physical object is an amount of matter (Pangloss) 2. An association is a group (WordNet)
3. An amount of matter is a physical object (Word
Net) 4. A place is a physical object (Mikrokosmos,
WordNet) C o n f u s i o n o f s e n s e s 5. A window is both an artifact and a place (Mikrokosmos) C l a s h o f s e n s e s 6. A person is both a physical object and a living being (Pangloss) 7. An animal is both a solid tangible thing and a perceptual agent (CYC) 8. A car is both a solid tangible thing and a physical device (CYC) 9. An organization is both a social-being and a group (CYC) 10. A communicative event is a physical, a mental, and a social event (Mikrokosmos, Penman) S u s p e c t t y p e - t o - r o l e l i n k 11. A person is both a living thing and a causal agent (WordNet) 12. An apple is both fruit and food (WordNet, CYC) These five classes of examples represent different kinds of IS-A overloading due to ontological misconceptions, which are discussed in turn.
In Examples 1-2, the ontological nature of the parent concept does not fully account for the nature of its child. A physical object is more than just an amount of matter, and an association is more than just a group of people: in fact, the same group of people could constitute different organizations. An analysis of the different identity conditions associated to these concepts leads to a different conceptualization, where an explicit constitution relation is taken into account.
This case is opposite to the previous one. Here is the parent concept's ontological nature that is weakened by a child whose nature is very different. Consider for instance WordNet's gloss for physical-object: object, physical object: a physical (tangible and visible) entity; “it was full of rackets, balls and other objects” [Wordnet 1.6] The sense of “physical object” implicit in these words seems to contradict the two examples reported, since: ii) “amount of matter” is an uncountable term, while the statement reported in the gloss refers to a countable notion of physical objects; i) a place is not tangible. We see therefore how these questionable IS-A links force a weaker interpretation of the subsuming concept.
C o n f u s i o n o f s e n s e s In Example 5, different senses of a word are collapsed into a single concept, inheriting from two parents. In WordNet, two different “synsets” are associated to the term window: one is subsumed by opening, and the other by panel. Here such distinction is not made, and polysemy is handled by multiple inheritance. While this choice may appear economical at a first sight, it presents in this case evident ontological difficulties: is there an entity that is both a panel and an opening? A cleaner solution is to represent the two senses as disjoint concepts, expressing their intrinsic connection by means of extra relations (for instance, the purpose of a window-panel is to cover a window-opening).
C l a s h o f s e n s e s In these examples of multiple inheritance, the parent concepts have incompatible meanings. Consider Example 6: in fact, one may think that a person has both the properties of physical objects and living beings. However, as we shall see, physical-object and living-being appear at a closer inspection as disjoint concepts, since they have no common identity criteria. So the situation is the same as in Example 5, with the difference that the link between the two senses is stronger: here a living being depends on a physical object (namely its body) for its existence (Figure 2). It is also constituted by it, since the body and the living being have the same parts. In WordNet, these two senses for “person” are recognized, but no explicit relationships hold between them.
Examples 7-8 are very similar to 6, since in both cases perceptual agents and physical devices have no identity criteria in common with solid tangible things. Example 9 is even more evident, since the same group of people can form different organizations. In Example 10 (Figure 5), three different senses are collapsed together, as if a communicative event was just a physical event with some extra properties. Indeed, a communication event involves some mental event as well as some physical event, but the identity criteria of these entities are different one each other, so they belong to disjoint concepts.
This last class of examples is different from the previous ones. In this case the two links involved in the multiple inheritance have a different “strength”: a person is necessarily a living thing, while her/he plays the role of causal agent only when involved in certain events. Analogously for the apple, which is necessarily a fruit while it can be a food. person and apple are types, while causal-agent and food are roles. As we shall see, person and apple are types, while causal-agent and food are roles. On the basis of ontological analysis, I shall bring a reason why forbidding a role to subsume a type. 3 . T h e Ro l e o f I d en t i t y C ri te ri a Let us focus first on the notion of identity criterion, which plays a fundamental role in our discussion. Briefly, we can say that an identity criterion (IC) for a property P is a binary relation IP such that (Noonan, 1993)
Px ∧ P y ∧ IPxy → x=y If, for a given property P, we are able to define such an IP, then we say that P carries an IC for its instances.
We see therefore that an IC determines a sufficient condition for identity. In practice, ICs for classes corresponding to natural language words are often difficult or impossible to express. However, it is relatively easy (and quite useful) to identify some necessary conditions for identity, which are required to: • classify an entity as an instance of a class C • individuate an entity as a countably distinct instance of
C • identify two entities at a given time (synchronic identity) • re-identify an instance of C across time (persistence, or diachronic identity) These conditions may involve the nature of the parts of a certain entity (e.g., the chemical constitution of water), the topological relationships among parts (e.g., the selfconnectedness of a stone), the relationships with regions of time/space (e.g. the occupancy of the same region of space), or the persistence of a certain global property across time (e.g., the permanence of a certain shape). It is important to take in mind that the decision of ascribing any of these conditions to a certain class is the result of our conceptualization of the world, i.e. of our ontology.
After these clarifications, let us see how ICs may affect
a taxonomic organization. Consider to this purpose the
example reported in
Within concrete objects, I assume here for granted the classical distinction between continuants and occurrents.
Continuants have a location in space, but this location can vary with time. They have spatial parts, but they do not have a temporal location, nor temporal parts. They always have other continuants as parts.
Occurrents are “generated” by continuants, according to the ways they behave in time. In order for an occurrent to exist, a specific continuant must take part to it. If the continuant changes its identity, the occurrent also changes its identity, so that continuants are rigidly dependent on continuants. Examples of occurrents are ordinary events like the change of location of a body, but also the permanence of a body in a given location (a state occurrence). Occurrents always have other occurrents as parts. They have a unique temporal location, while their exact spatial location is often not clear.
O n t o l o g i c a l L e v e l s Let us see now how, by applying Lowe’s principle, we can introduce systematic distinctions among ontological categories that overcome the IS-A overloading problems mentioned earlier.
Take for instance a person, which can be conceptualized as an intentional agent, a living being or just a physical object (see Example 6). I argue that, since these concepts imply different ICs, they correspond to disjoint categories: three distinct individuals, instances of the three concepts above, share a common spatial location. Since the person depends on the underlying biological organism, as well as the latter depends on the underlying amount of matter, there is an intrinsic order within these categories, which belong therefore to different ontological levels.
A dependence relation links higher levels to lower levels: an animal depends on its body, which depends on body parts having a certain functionality, which depend on pieces of matter having specific properties, and so on.
Atomic Static Mereological Physical
Topological
Morphological Functional Biological Intentional Social (a minimal grain of matter) (a configuration) (an amount of matter) (a piece of matter) (a cubic block) (an artifact) (a human body) (a person or a robot) (a company)
We have therefore a classification of ontological levels based on different kinds of IC (Figure 4), corresponding to different sets of individuation and persistence conditions. Each level corresponds to a class of ICs. These classes are assumed to describe disjoint sets of entities, in accordance with Lowe’s principle. They are orthogonal to the continuants/occurrents distinction introduced above.
At the atomic level, we consider entities having minimal spatial or temporal dimensions, according to a certain granularity dependent on our conceptualization. We assume spatio-temporal continuity as a necessary condition for their identity.
At the static level, all the non-temporal properties of a particular contribute to its identity: if one of these changes, identity is lost. In this level only very peculiar objects are defined, namely configurations of atoms and situations (occurrences of configurations). The former are continuants, the latter are occurrents.
At the mereological level, the IC is extensional: two entities are the same if and only if they have the same parts (mereological essentialism). Regions of space, temporal intervals and amounts of matter belong to this level. Subsequent levels are characterized by an intensional criterion of identity, in the sense that mereological identity is neither sufficient nor necessary for identity.
The physical level corresponds to ICs bound to spatial configuration of matter (i.e., to topo-morphological properties). It can be split into two separate layers.
At the topological layer, the IC is bound to topological properties: for instance, topological self-connection can be considered as a necessary property to maintain identity: a piece of matter belongs to this layer, while a (possibly disconnected) amount of matter belongs to the mereological level. The two things are distinct entities, since a piece of matter can cease to exist (generating new pieces) while the same amount of matter is still there. At the morphological layer, the IC is bound to morphological properties (or, in general, gestaltic properties related to spatial proximity), like spatial shapes or temporal patterns. A change of these properties can influence identity. A cube-shaped block is an example of an instance of this level: if its shape changes (above a certain limit) it is not the same cube any more, while still being the same piece of matter.
The levels above the physical level are related to ICs bound to the way objects interact with the external world. At the functional level, the IC is bound to functional and pragmatic properties: identity is destroyed when functionality is destroyed. At the biological level, the IC is bound to properties related to life: identity is destroyed when biological activity ceases. At the intentional level, the IC is bound to capability of intentional behavior: identity is destroyed when such capability ceases. At the social level, the IC is bound to social rules and conventions involving the interaction of intentional objects. Identity is destroyed when some of these rules change.
social-event mental-event physical-event social-event communication-event perceptual-event communication-event mental-event
perceptual-event physical-event
In conclusion, we can see how the adoption of Lowe's
principle and the introduction of ontological levels solves
the IS-A overloading problems discussed earlier (at least
for examples 1-10). In all these cases, the proposed
solution is the introduction of disjoint concepts (belonging to
different ontological levels) accounting for the different
senses involved (Figure 5). The costs of this choice are: i)
a moderate proliferation (by a constant factor
corresponding to the number of levels) of the number of entities in
the domain; ii) the necessity to take into account different
relations besides IS-A, such as dependence,
spatiotemporal colocalization and constitution relations of
various kinds. A formal characterization of these relations is
outside the scope of this paper. See
Category (location, object) (-I +R) Role (~R +D)
Material role (student) (+I)
Formal role (patient, part) (-I)
Attribution (red, decomposable) (-I -R -D)
Relation (part-of)
The purpose of studying the distinctions among properties is twofold. On one hand, we are interested in assessing their organizational role in a taxonomy, that is their practical relevance as taxons, i.e. nodes of a taxonomy; on the other hand, we want to study their attitude to generate clean and understandable hierarchies, with a minimum degree of “tangleness”. With the help of formal ontology, we can characterize such distinctions on the basis of the following meta-properties: 1. Identity (+I). The property of carrying an IC. 2. Rigidity (+R). A property P is rigid if, for each x, if P(x) is true in one possible world, then it is also true in all possible worlds. Person and location are rigid, while student and tall are not. 3. Anti-rigidity (~R)2. A property P is anti-rigid if, for each x, P(x) is true in one possible world, and false in a different possible world. Student and tall are both nonrigid (-R) and anti-rigid (~R). 4. Dependence (+D). A property P is dependent if, necessarily, whenever P(x) holds, then Q(y) holds, with x ≠ y and P ≠ Q (see the class dependence mentioned before). Father is dependent, person is not.
A type is a property that is rigid and carries an IC. Types
play the most important organizational role in a
taxonomy. Assuming that each type has a distinct set of ICs,
2 See
A category is a property that is also rigid but does not carry a specific IC. Since they cannot be subsumed by types (otherwise they would have an IC), categories only appear in the uppermost levels of a taxonomy. Their role is to make clear the most general distinctions.
life-form entity person * causal-agent ?
Types and categories are both rigid, and can be either dependent or independent (person is independent, event is dependent). A role is a property that is anti-rigid and is always dependent3. Material roles like student do have an IC, while formal roles like part do not. However, the IC of material roles is only indirect, since they do not introduce any specific IC, but rather they inherit it from a subsuming type. No explicit mutual disjointness assumption is made for roles, as they tend to generate tangled hierarchies. They have for this reason a limited organizational relevance. It seems therefore advisable to explicitly distinguish roles from types in order to easily isolate the main backbone of a taxonomy, and to perform inferences related to mutual disjointness (Figure 7). Notice that a role cannot subsume a type, since the former is anti-rigid and the latter is rigid.
Finally, an attribution is a property that is not rigid, is not dependent, and does not carry any IC4. Attributions do not seem to play any useful organizational role in the on3 This account of roles in terms of rigidity seems to work well, but it requires some philosophical care with concepts like child: in order for child to be anti-rigid, there must exist for each person a world where such a person is not a child. This world can be imagined as the one where this person is the first person on the Earth. 4 This term is introduced in order to avoid confusion with the term attribute, largely used in knowledge representation and modelling languages. Color, part, father may be attributes, while red is an attribution (in this case, an attribute-value). tology of particulars, as they may hold for disparate kinds of entity. Hence, they should not appear as taxons there, while the related information can be contained within the definitions of taxons whose instances exhibit such attribution. We see therefore how with this choice we solve the problems of confusion of organizational roles mentioned at the beginning of this paper. 6 . S o m e B a s i c D e s i g n P ri n c i pl e s In conclusion, let us summarize the ontology design principles emerging from this discussion, which can solve the ISA overloading problems we have mentioned in precedence. 1. Be clear about the domain. Any formal theory is a theory about a domain. Such a domain must be clarified in advance. In particular, in our case, it is very important to make clear whether the entities we speak of (i.e., the instances of our classes) are: • particulars; • universals, i.e. conceptual properties and relations; • linguistic entities like nouns, verbs or adjectives. What I have suggested is to have two separate ontologies for particulars and universals, keeping lexical items out of the domain. 2. Take identity seriously. We have seen how the notion of identity criterion (and especially Lowe’s principle) can play a crucial role in clarifying ontological distinctions. 3. Isolate a basic taxonomic structure. We have seen how the notion of “basic backbone” acquires a rigorous meaning, being constituted by categories and types. Under the assumption of having each one a different set of ICs, types form a tree of mutually disjoint classes. We can reasonably assume, as a design principle, that also categories form a (very shallow) tree of mutually disjoint classes. 4. Identify roles explicitly. We have seen that an explicit tag for roles has two advantages: i) you can easily hide them in order to isolate the basic backbone; ii) you can perform inferences involving mutual disjointness while avoiding explicit declarations, unless for cases like sondaughter, where two roles are linked by an antonym link. A c kn o w l ed g e m en t s