The Role of Identity Conditions in Ontology Design Nicola Guarino National Research Council LADSEB-CNR, Padova, Italy guarino@ladseb.pd.cnr.it http://www.ladseb.pd.cnr.it/infor/ontology/ontology.html Abs tract I will focus here on a single design practice, which is the main responsible of most semantic difficulties: IS-A Cur rent ont ologi es' upp er-le vel tax onomi c overloading. Notice that I do not refer with this expression str uctur e is oft en qui te com plica ted and har d to to the old debate about the semantics of IS-A (Brachman, und ersta nd. In thi s pap er I sho w how the the o- 1983), since I assume a standard set-inclusion semantics ret ical too ls of so- calle d For mal Ont ology , and for it. Rather, I will discuss the cases where this standard esp ecial ly the the ory of ide ntity , can hel p to semantics turns out to be violated, if we carefully analyze for mulat e cle aner, mor e gen eral, mor e rig or- the ontological nature of the arguments. I will consider a ous , and mor e und ersta ndabl e upp er-le vel on- number of "bad practice" cases, proposing a way to sim- tol ogies . I foc us in par ticul ar on som e exa m- plify the domain's hierarchical structure by splitting some ple s of mul tiple gen erali zatio n, pro posin g a concepts according to different identity conditions, or by way of sim plify ing the dom ain str uctur e by excluding them from an explicit representation because of spl ittin g som e con cepts acc ordin g to dif feren t their limited taxonomic role. Among other things, I will ide ntity con ditio ns, or by exc ludin g the m be- criticize the use of multiple inheritance to account for cau se of the ir lim ited org aniza tiona l rol e. polysemic phenomena, arguing for the necessity of better understanding their underlying ontological structure, with 1. Introduction a goal similar to that of [Pustejovsky, 1995 #349; Puste- Currently, a number of efforts in the area of knowledge jovsky, 1998 #407]. and language engineering are aimed to the development of systems of basic semantic categories (often called "upper- level ontologies"), to be used for various applications such as natural-language processing, multilingual infor- mation retrieval, information integration, intelligent sys- tems design. Examples of such systems are CYC's upper level, Penman's Upper Model (Bateman et al., 1990), re- cently evolved into the Pangloss ontology (Knight & Luk, 1994) and the Revised Upper Model (Bateman, 1995), the Mikrokosmos ontology (Mahesh, 1996), and Figure 1. An example of multiple inheritance in Pangloss. WordNet's upper structure (Miller, 1995). Unfortunately, the upper-level taxonomic structure of these ontologies is often quite complicated and hard to understand. 2. The Main Problem: IS-A Overloading This paper intends to show how the theoretical tools of All ontologies are centered on a taxonomy, based on a par- so-called Formal Ontology (Guarino, 1995)—and espe- tial ordering relation named in various ways. Such taxon- cially the Theory of Identity—can help to formulate some omy is the ontology's main backbone, which can be ontological distinctions and design principles able to pro- “fleshed” with the addition of attributes and other relations duce cleaner, more general, more rigorous and at the same among nodes. As usual, we shall generically call IS-A time more understandable upper-level ontologies. such taxonomic relation (not to be confused with In- stanceOf, which links a node to the class it belongs to and The copyright of this paper belongs to the papers authors. Permission to is not a partial order). IS-A's semantics will be the stan- copy without fee all or part of this material is granted provided that the dard one: if P and Q are unary predicate symbols, P IS-A copies are not made or distributed for direct commercial advantage. Q iff I(P) ⊆ I(Q), where I is an interpretation function Proceedings of the IJCAI-99 workshop on mapping unary predicates into subsets of the domain. Ontologies and Problem-Solving Methods (KRR5) One of the problems with IS-A when considering lin- Stockholm, Sweden, August 2, 1999 guistic ontologies like WordNet is that it often reflects a (V.R. Benjamins, B. Chandrasekaran, A. Gomez-Perez, N. Guarino, lexical relation between words, rather than an ontological M. Uschold, eds.) relation between classes of domain entities. Although this http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-18/ N. Guarino 2-1 fact is well known, the tendency to confuse the two as- physical object is more than just an amount of matter, and pects is quite high, especially when linguistic ontologies an association is more than just a group of people: in fact, are used for non-linguistic applications. For instance, a the same group of people could constitute different organi- common habit in linguistic ontologies is to rely on mul- zations. An analysis of the different identity conditions as- tiple inheritance for representing polysemy, as in the case sociated to these concepts leads to a different conceptuali- of Figure 1. This results in an overloading of IS-A's role, zation, where an explicit constitution relation is taken which, as we shall see, may cause serious semantic prob- into account. lems. To overcome these problems, the solution I propose is Overgeneralization to pay more attention to the ontological implications of This case is opposite to the previous one. Here is the par- taxonomic choices, limiting IS-A links to connect nodes ent concept's ontological nature that is weakened by a sharing a common identity criterion. In this way, the tax- child whose nature is very different. Consider for instance onomy reflects a basic ontological structure with a clear WordNet's gloss for physical-object: semantics, while the extra-information currently encoded by IS-A links can be represented by means of specialized links and attributes. object, physical object: a physical (tangible and visible) I will consider the following examples of IS-A links: entity; “it was full of rackets, balls and other objects” [Wordnet 1.6] Reduction of sense The sense of “physical object” implicit in these words 1. A physical object is an amount of matter (Pan- seems to contradict the two examples reported, since: ii) gloss) “amount of matter” is an uncountable term, while the 2. An association is a group (WordNet) statement reported in the gloss refers to a countable notion of physical objects; i) a place is not tangible. We see Overgeneralization therefore how these questionable IS-A links force a weaker 3. An amount of matter is a physical object (Word- interpretation of the subsuming concept. Net) 4. A place is a physical object (Mikrokosmos, Confusion of senses WordNet) In Example 5, different senses of a word are collapsed into Confusion of senses a single concept, inheriting from two parents. In Word- 5. A window is both an artifact and a place (Mik- Net, two different “synsets” are associated to the term rokosmos) window: one is subsumed by opening, and the other by panel. Here such distinction is not made, and polysemy Clash of senses is handled by multiple inheritance. While this choice may 6. A person is both a physical object and a living be- appear economical at a first sight, it presents in this case ing (Pangloss) evident ontological difficulties: is there an entity that is 7. An animal is both a solid tangible thing and a both a panel and an opening? A cleaner solution is to rep- perceptual agent (CYC) resent the two senses as disjoint concepts, expressing their 8. A car is both a solid tangible thing and a physical intrinsic connection by means of extra relations (for in- device (CYC) stance, the purpose of a window-panel is to cover a win- 9. An organization is both a social-being and a group dow-opening). (CYC) 10. A communicative event is a physical, a mental, Clash of senses and a social event (Mikrokosmos, Penman) In these examples of multiple inheritance, the parent con- cepts have incompatible meanings. Consider Example 6: Suspect type-to-role link in fact, one may think that a person has both the proper- 11. A person is both a living thing and a causal agent ties of physical objects and living beings. However, as we (WordNet) shall see, physical-object and living-being appear at 12. An apple is both fruit and food (WordNet, CYC) a closer inspection as disjoint concepts, since they have no common identity criteria. So the situation is the same These five classes of examples represent different kinds of as in Example 5, with the difference that the link between IS-A overloading due to ontological misconceptions, the two senses is stronger: here a living being depends on which are discussed in turn. a physical object (namely its body) for its existence (Figure 2). It is also constituted by it, since the body and Reduction of sense the living being have the same parts. In WordNet, these In Examples 1-2, the ontological nature of the parent con- two senses for “person” are recognized, but no explicit re- cept does not fully account for the nature of its child. A lationships hold between them. N. Guarino 2-2 Examples 7-8 are very similar to 6, since in both cases • classify an entity as an instance of a class C perceptual agents and physical devices have no identity cri- teria in common with solid tangible things. Example 9 is • individuate an entity as a countably distinct instance of even more evident, since the same group of people can C form different organizations. In Example 10 (Figure 5), • identify two entities at a given time (synchronic iden- three different senses are collapsed together, as if a com- tity) municative event was just a physical event with some ex- • re-identify an instance of C across time (persistence, or tra properties. Indeed, a communication event involves diachronic identity) some mental event as well as some physical event, but the identity criteria of these entities are different one each These conditions may involve the nature of the parts of a other, so they belong to disjoint concepts. certain entity (e.g., the chemical constitution of water), the topological relationships among parts (e.g., the self- connectedness 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 (Lowe, 1989): should ordered-set Figure 2. The multiple links of Fig. 1 have been eliminated be subsumed by set? Despite the apparent answer to this by introducing disjoint concepts for the different senses of question is "yes", after some thoughts we recognize it person. Dashed arrows represent dependence links, account- cannot be the case, because of cardinality reasons (multi- ing for the relationship between these senses. ple different ordered-sets may correspond to the same ordi- nary set). This is because the two concepts do not have an Suspect type-to-role link. IC in common: having the same members is a sufficient condition for the identity of sets, but not for the identity This last class of examples is different from the previous of ordered sets1. For analogous reasons, organization ones. In this case the two links involved in the multiple should not be subsumed by group, and person should not inheritance have a different “strength”: a person is neces- be subsumed by physical object (as a physical object, sarily a living thing, while her/he plays the role of causal a body has persistence conditions different from a living agent only when involved in certain events. Analogously being). Jonathan Lowe (1989) has discussed these prob- for the apple, which is necessarily a fruit while it can be a lems at length, defending the following principle: 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 “No individual can instantiate both of two sorts if the basis of ontological analysis, I shall bring a reason they have different criteria of identity associated why forbidding a role to subsume a type. with them”. (Lowe, 1989) 3 . T h e Ro l e of I d en t i t y C r i te r i a I assume this as the basic principle to be adopted for well- Let us focus first on the notion of identity criterion, founded ontologies. 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 I P such that (Noonan, 1993) Px ∧ Py ∧ IPxy → x=y 1 If, for a given property P, we are able to define such an IP, We may observe that, according to Kuratowski's definition, then we say that P carries an IC for its instances. the ordered set can be written as {{a},{a,b}}. In this We see therefore that an IC determines a sufficient con- case, denying that an ordered set is a set would be difficult. dition for identity. In practice, ICs for classes correspond- Lowe however underlines that this "definition" establishes a ing to natural language words are often difficult or impos- useful mathematical correspondence between ordinary sets sible to express. However, it is relatively easy (and quite and ordered sets, but it can hardly be considered as an onto- useful) to identify some necessary conditions for identity, logical definition, since it does not give an account of the no- which are required to: tion of "member" of an ordered set. This example however does not influence the main argument. N. Guarino 2-3 4. A Minimal Ontology of Particulars concepts imply different ICs, they correspond to disjoint categories: three distinct individuals, instances of the three In order to address the problems discussed in the introduc- concepts above, share a common spatial location. Since tion, we have to clarify first our minimal ontological the person depends on the underlying biological organism, commitments. I assume a distinction between as well as the latter depends on the underlying amount of matter, there is an intrinsic order within these categories, • the entities of the world to be included in our domain which belong therefore to different ontological levels. of discourse, or particulars A dependence relation links higher levels to lower lev- • the properties and relations used to talk about such els: an animal depends on its body, which depends on entities, or universals body parts having a certain functionality, which depend on pieces of matter having specific properties, and so on. I will quickly present below what I consider the “basic backbones” of these ontologies, with the only purpose of making clear the methodological discussion which fol- Atomic (a minimal grain of matter) lows. Static (a configuration) Mereological (an amount of matter) Physical Particular Topological (a piece of matter) Location Morphological (a cubic block) Space (a spatial region) Functional (an artifact) Time (a temporal region) Biological (a human body) Object Intentional (a person or a robot) Concrete object Social (a company) Continuant (an apple) Occurrent (the fall of an apple) Figure 4. Ontological levels correspond to disjoint sets of Abstract object (Pythagoras’ theorem) particulars, according to the different ICs adopted to concep- Figure 3. The basic backbone of the ontology of particulars. tualize them. The first distinction among particulars is between objects We have therefore a classification of ontological levels and locations. A location is either a region of (absolute) based on different kinds of IC (Figure 4), corresponding to space or an interval of (absolute) time. An object is a par- different sets of individuation and persistence conditions. ticular which is not a location. Objects are concrete if they Each level corresponds to a class of ICs. These classes are have a location in time and/or in space, abstract otherwise. assumed to describe disjoint sets of entities, in accordance Within concrete objects, I assume here for granted the with Lowe’s principle. They are orthogonal to the contin- classical distinction between continuants and occurrents. uants/occurrents distinction introduced above. Continuants have a location in space, but this location At the atomic level, we consider entities having mini- can vary with time. They have spatial parts, but they do mal spatial or temporal dimensions, according to a certain not have a temporal location, nor temporal parts. They granularity dependent on our conceptualization. We as- always have other continuants as parts. sume spatio-temporal continuity as a necessary condition Occurrents are “generated” by continuants, according to for their identity. the ways they behave in time. In order for an occurrent to At the static level, all the non-temporal properties of a exist, a specific continuant must take part to it. If the con- particular contribute to its identity: if one of these tinuant changes its identity, the occurrent also changes its changes, identity is lost. In this level only very peculiar identity, so that continuants are rigidly dependent on con- objects are defined, namely configurations of atoms and tinuants. Examples of occurrents are ordinary events like situations (occurrences of configurations). The former are the change of location of a body, but also the permanence continuants, the latter are occurrents. of a body in a given location (a state occurrence). Occur- At the mereological level, the IC is extensional: two rents always have other occurrents as parts. They have a entities are the same if and only if they have the same unique temporal location, while their exact spatial loca- parts (mereological essentialism). Regions of space, tem- tion is often not clear. poral intervals and amounts of matter belong to this level. Subsequent levels are characterized by an intensional crite- Ontological Levels rion of identity, in the sense that mereological identity is neither sufficient nor necessary for identity. Let us see now how, by applying Lowe’s principle, we The physical level corresponds to ICs bound to spatial can introduce systematic distinctions among ontological configuration of matter (i.e., to topo-morphological prop- categories that overcome the IS-A overloading problems erties). It can be split into two separate layers. mentioned earlier. At the topological layer, the IC is bound to topologi- Take for instance a person, which can be conceptual- cal properties: for instance, topological self-connection ized as an intentional agent, a living being or just a can be considered as a necessary property to maintain iden- physical object (see Example 6). I argue that, since these tity: a piece of matter belongs to this layer, while a (pos- N. Guarino 2-4 sibly disconnected) amount of matter belongs to the mere- 5. A Minimal Ontology of Universals ological level. The two things are distinct entities, since a piece of matter can cease to exist (generating new pieces) A minimal ontology of universals, based on a revision of while the same amount of matter is still there. At (Guarino, Carrara & Giaretta, 1994), is reported in Figure the morphological layer, the IC is bound to morphologi- 6. The first distinction is the usual one between properties cal properties (or, in general, gestaltic properties related to and relations, according to the number of arguments. We spatial proximity), like spatial shapes or temporal pat- only focus on primitive properties, which are not obtain- terns. A change of these properties can influence identity. able by Boolean combination of other properties. 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 Universal of matter. Property The levels above the physical level are related to ICs Type (person) (+I +R) bound to the way objects interact with the external world. Category (location, object) (-I +R) At the functional level, the IC is bound to functional and Role (~R +D) pragmatic properties: identity is destroyed when function- Material role (student) (+I) ality is destroyed. At the biological level, the IC is bound Formal role (patient, part) (-I) to properties related to life: identity is destroyed when bio- Attribution (red, decomposable) (-I -R -D) logical activity ceases. At the intentional level, the IC is Relation (part-of) bound to capability of intentional behavior: identity is de- stroyed when such capability ceases. At the social level, Figure 6. The basic backbone of the ontology of universals. I the IC is bound to social rules and conventions involving = identity, R = rigidity, D = dependence. the interaction of intentional objects. Identity is destroyed when some of these rules change. 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 prac- social-event communication-event tical relevance as taxons, i.e. nodes of a taxonomy; on the mental-event other hand, we want to study their attitude to generate perceptual-event clean and understandable hierarchies, with a minimum de- physical-event gree of “tangleness”. With the help of formal ontology, we can characterize such distinctions on the basis of the social-event communication-event following meta-properties: mental-event perceptual-event 1. Identity (+I). The property of carrying an IC. 2. Rigidity (+R). A property P is rigid if, for each x, if physical-event P(x) is true in one possible world, then it is also true in all possible worlds. Person and location are rigid, Figure 5. Above: communication and perceptual events in while student and tall are not. Mikrokosmos. Below: the simplification resulting from the 3. Anti-rigidity (~R)2. A property P is anti-rigid if, for assumption of ontological levels. Dashed arrows denote the each x, P(x) is true in one possible world, and false in dependence relation. a different possible world. Student and tall are both nonrigid (-R) and anti-rigid (~R). In conclusion, we can see how the adoption of Lowe's 4. Dependence (+D). A property P is dependent if, nec- principle and the introduction of ontological levels solves essarily, whenever P(x) holds, then Q(y) holds, with the IS-A overloading problems discussed earlier (at least x ≠ y and P ≠ Q (see the class dependence mentioned for examples 1-10). In all these cases, the proposed solu- before). Father is dependent, person is not. tion 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 type is a property that is rigid and carries an IC. Types a moderate proliferation (by a constant factor correspond- play the most important organizational role in a taxon- ing to the number of levels) of the number of entities in omy. Assuming that each type has a distinct set of ICs, the domain; ii) the necessity to take into account different relations besides IS-A, such as dependence, spatio- 2 See (Guarino, 1992; Guarino, Carrara & Giaretta, 1994) for a temporal colocalization and constitution relations of vari- technical account of ontological rigidity and for a characteri- ous kinds. A formal characterization of these relations is zation of roles as non-rigid entities. The notion of anti- outside the scope of this paper. See (Simons, 1987; Fine, rigidity introduced here seems to better account for the onto- 1995; Casati & Varzi, 1999) for a thorough technical dis- logical nature of roles, and explains the issue discussed in cussion on these issues. Figure 7. N. Guarino 2-5 we have that, according to Lowe’s principle, a taxonomy tology of particulars, as they may hold for disparate kinds of types is always a tree. When a type specializes another of entity. Hence, they should not appear as taxons there, type, it adds further ICs to those carried by the subsuming while the related information can be contained within the type. For instance, when the type triangle specializes definitions of taxons whose instances exhibit such attribu- polygon, it adds the ICs based on the equivalence of two tion. We see therefore how with this choice we solve the sides and one angle (or two angles and one side) to those problems of confusion of organizational roles mentioned proper of polygons (same sides and same angles). at the beginning of this paper. A category is a property that is also rigid but does not carry a specific IC. Since they cannot be subsumed by 6 . S o m e B a s i c D e s ig n P ri n c i pl e s types (otherwise they would have an IC), categories only appear in the uppermost levels of a taxonomy. Their role In conclusion, let us summarize the ontology design prin- is to make clear the most general distinctions. ciples emerging from this discussion, which can solve the ISA overloading problems we have mentioned in prece- entity dence. 1. Be clear about the domain. Any formal theory is a the- life-form * causal-agent ory about a domain. Such a domain must be clarified in advance. In particular, in our case, it is very important to ? person make clear whether the entities we speak of (i.e., the in- stances of our classes) are: African European * worker • particulars; • universals, i.e. conceptual properties and relations; Figure 7. Types and roles in WordNet (roles marked with *). • linguistic entities like nouns, verbs or adjectives. While it is OK for a type to subsume a role, the vice versa is forbidden according to the semantics we have given. Notice that, being types, African and European are disjoint. What I have suggested is to have two separate ontologies for particulars and universals, keeping lexical items out of Types and categories are both rigid, and can be either the domain. dependent or independent (person is independent, event is dependent). A role is a property that is anti-rigid and is 2. Take identity seriously. We have seen how the notion always dependent3. Material roles like student do have an of identity criterion (and especially Lowe’s principle) can IC, while formal roles like part do not. However, the IC play a crucial role in clarifying ontological distinctions. of material roles is only indirect, since they do not intro- duce any specific IC, but rather they inherit it from a sub- 3. Isolate a basic taxonomic structure. We have seen how suming type. No explicit mutual disjointness assumption the notion of “basic backbone” acquires a rigorous mean- is made for roles, as they tend to generate tangled hierar- chies. They have for this reason a limited organizational ing, being constituted by categories and types. Under the relevance. It seems therefore advisable to explicitly distin- assumption of having each one a different set of ICs, guish roles from types in order to easily isolate the main types form a tree of mutually disjoint classes. We can rea- backbone of a taxonomy, and to perform inferences related sonably assume, as a design principle, that also categories to mutual disjointness (Figure 7). Notice that a role can- form a (very shallow) tree of mutually disjoint classes. not subsume a type, since the former is anti-rigid and the latter is rigid. 4. Identify roles explicitly. We have seen that an explicit Finally, an attribution is a property that is not rigid, is tag for roles has two advantages: i) you can easily hide not dependent, and does not carry any IC4. Attributions do them in order to isolate the basic backbone; ii) you can not seem to play any useful organizational role in the on- perform inferences involving mutual disjointness while avoiding explicit declarations, unless for cases like son- 3 This account of roles in terms of rigidity seems to work daughter, where two roles are linked by an antonym link. well, but it requires some philosophical care with concepts like child: in order for child to be anti-rigid, there must exist A c kn o w l ed g e m en t s 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 I wish to thank Stefano Borgo, Massimiliano Carrara, the first person on the Earth. Pierdaniele Giaretta, Claudio Masolo, Barry Smith, 4 This term is introduced in order to avoid confusion with the Achille Varzi. 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). N. Guarino 2-6 R e fe r e n ce s Bateman, J. A. 1995. On the Relationship Between On- tology Construction and Natural Language: a Socio- Semiotic View. International Journal of Human- Computer Studies, 43: 929-944. Bateman, J. A., Kasper, R. T., Moore, J. D., and Whit- ney, R. A. 1990. A General Organization of Knowledge for Natural Language Processing: the PENMAN upper model. USC/Information Sciences Institute, Marina del Rey, CA. Brachman, R. 1983. What IS-A Is and Isn't: An Analysis of Taxonomic Links in Semantic Networks. IEEE Computer, 16(10): 30-36. Casati, R. and Varzi, A. 1999. Parts and Places. The Structure of Spatial Representation. MIT Press, Cam- bridge, MA. Fine, K. 1995. Ontological Dependence. Proceedings of the Aristotelian Society, 95: 269-90. Guarino, N. 1992. Concepts, Attributes and Arbitrary Re- lations: Some Linguistic and Ontological Criteria for Structuring Knowledge Bases. Data & Knowledge En- gineering, 8(2): 249-261. Guarino, N. 1995. Formal Ontology, Conceptual Analy- sis and Knowledge Representation. International Journal of Human and Computer Studies, 43(5/6): 625-640. Guarino, N., Carrara, M., and Giaretta, P. 1994. An On- tology of Meta-Level Categories. In D. J., E. Sandewall and P. Torasso (eds.), Principles of Knowledge Repre- sentation and Reasoning: Proceedings of the Fourth In- ternational Conference (KR94). Morgan Kaufmann, San Mateo, CA: 270-280. Knight, K. and Luk, S. 1994. Building a Large Knowl- edge Base for Machine Translation. In Proceedings of American Association of Artificial Intelligence Confer- ence (AAAI-94). Seattle, WA: 773-778. Lowe, E. J. 1989. Kinds of Being. A Study of Individua- tion, Identity and the Logic of Sortal Terms. Basil Blackwell, Oxford. Mahesh, K. 1996. Ontology Development for Machine Translation: Ideology and Methodology. New Mexico State University, Computing Research Laboratory MCCS-96-292. Miller, G. A. 1995. WORDNET: A Lexical Database for English. Communications of ACM, 2(11): 39-41. Noonan, H. 1993. Introduction. In H. Noonan (ed.) Id- enity. Dartmouth, Aldershot: xi-xx. Simons, P. 1987. Parts: a Study in Ontology. Clarendon Press, Oxford. N. Guarino 2-7