CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011 Representing Concepts in Artificial Systems: A Clash of Requirements Marcello Frixione (mfrixione@unisa.it), Antonio Lieto (alieto@unisa.it) Department of Political, Social and Communication Sciences University of Salerno, Italy Abstract are conceived in philosophy and in psychology. In section 3. we argue that AI research in some way shows The problem of concept representation is relevant for many traces of the contradictions individuated in sect. 2. In subfields of cognitive research, including psychology, particular, the requirement of compositional, logical style philosophy and artificial intelligence. In particular, in semantics conflicts with the need of representing recent years, it received great attention within knowledge representation, because of its relevance for knowledge concepts in the terms of typical traits that allow for engineering and for ontology-based technologies. exceptions. In section 4 we review some attempts to However, the notion of concept itself turns out to be highly resolve this conflict in the field of knowledge disputed and problematic. In our opinion, one of the causes representation, with particular attention to description of this state of affairs is that the notion of concept is in logics. It is our opinion that a mature methodology to some sense heterogeneous, and encompasses different approach knowledge representation and knowledge cognitive phenomena. This results in a strain between engineering should take advantage from both the conflicting requirements, such as, for example, empirical results of cognitive psychology that concern compositionality on the one side and the need of human abilities and from philosophical analyses. In this representing prototypical information on the other. AI research in some way shows traces of this situation. In this spirit, in section 5 we individuate some possible paper we propose an analysis of this state of affairs. Since suggestions coming from different aspects of cognitive it is our opinion that a mature methodology to approach research: the distinction between two different types of knowledge representation and knowledge engineering reasoning processes, developed within the context of the should take advantage also from the empirical results of so-called “dual process” accounts of reasoning; the cognitive psychology concerning human abilities, we proposal to keep prototypical effects separate from sketch some proposal for concept representation in formal compositional representation of concepts; the possibility ontologies, which takes into account suggestions coming to develop hybrid, prototype and exemplar-based from psychological research. Our basic assumption is that representations of concepts. We conclude this article knowledge representation technologies designed considering evidences coming from experimental (section 6) with some tentative suggestion to implement psychology (and, therefore, more similar to the humans the above mentioned proposals within the context of way of reasoning and organizing information) can have semantic web languages, in terms of the linked data better results in real life applications (e.g. in the field of perspective. Semantic Web). Introduction 2 Concepts in Philosophy and in Psychology Computational representation of concepts is a central problem for the development of ontologies and for Within the field of cognitive science, the notion of knowledge engineering. Concept representation is a concept is highly disputed and problematic. Artificial multidisciplinary topic of research that involves such intelligence (from now on AI) and, more in general, the different disciplines as Artificial Intelligence, Philosophy, computational approach to cognition reflect this state of Cognitive Psychology and, more in general, Cognitive affairs. Conceptual representation seems to be Science. However, the notion of concept itself results to constrained by conflicting requirements, such as, for be highly disputed and problematic. In our opinion, one example, compositionality on the one side and the need of the causes of this state of affairs is that the notion itself of representing prototypical information on the other. of concept is in some sense heterogeneous, and A first problem (or, better, a first symptom that encompasses different cognitive phenomena. This results some problem exists) consists in the fact that the use of in a strain between conflicting requirements, such as, for the term “concept” in the philosophical tradition is not example, compositionality on the one side and the need homogeneous with the use of the same term in empirical of representing prototypical information on the other. psychology (see e.g. Dell’Anna and Frixione 2010). This has several consequences for the practice of Briefly1, we could say that in cognitive psychology a knowledge engineering and for the technology of formal ontologies. 1 In this paper we propose an analysis of this Things are made more complex by the fact that also within the situation. The paper is organised as follows. In section 2. two fields considered separately this notion is used in a we point out some differences between the way concepts heterogeneous way, as we shall synthetically see in the following. As a consequence, the following characterisation of 75 CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011 concept is essentially intended as the mental psychological treatments of concepts. On the other hand, representations of a category, and the emphasis is on such it is well known that compositionality is at odds with processes as categorisation, induction and learning. prototypicality effects, which are crucial in most According to philosophers, concepts are above all the psychological characterisations of concepts. components of thoughts. Even if we leave aside the Let us consider first the compositionality problem of specifying what thoughts exactly are, this requirement. In a compositional system of representations requires a more demanding notion of concept. In other we can distinguish between a set of primitive, or atomic words, some phenomena that are classified as symbols, and a set of complex symbols. Complex symbols “conceptual” by psychologists turn out to be are generated starting from primitive symbols through the “nonconceptual” for philosophers. There are, thus, mental application of a set of suitable recursive syntactic rules representations of categories that philosophers would not (usually, starting from a finite set of primitive symbols, a consider genuine concepts. For example, according to potentially infinite set of complex symbols can be many philosophers, concept possession involves the generated). Natural languages are the paradigmatic ability to make explicit, high level inferences, and example of compositional systems: primitive symbols sometimes also the ability to justify them (Peacocke correspond to the elements of the lexicon (or, better, to 1992; Brandom 1994). This clearly exceeds the morphemes), and complex symbols include the possession of the mere mental representation of (potentially infinite) set of all sentences. categories. Moreover, according to some philosophers, In compositional systems the meaning of a concepts can be attributed only to agents who can use complex symbol s functionally depends on the syntactic natural language (i.e., only adult human beings). On the structure of s and from the meaning of primitive symbols other hand, a position that can be considered in some in it. In other words, the meaning of complex symbols sense representative of an “extremist” version of the can be determined by means of recursive semantic rules psychological attitude towards concepts is expressed by that work in parallel with syntactic composition rules. In Lawrence Barsalou in an article symptomatically entitled this consists the so-called principle of compositionality of “Continuity of the conceptual system across species” meaning, which Gottlob Frege identified as one of the (Barsalou 2005). He refers to knowledge of scream main features of human natural languages. situations in macaques, which involves different In classical cognitive science it is often assumed modality-specific systems (auditory, visual, affective that mental representations are compositional. One of the systems, etc.). Barsalou interprets these data in favour of most clear and explicit formulation of this assumption is the thesis of a continuity of conceptual representations in due to Jerry Fodor and Zenon Pylyshyn (1988). They different animal species, in particular between humans claim that compositionality of mental representations is and non-human mammals: “this same basic architecture mandatory in order to explain some fundamental for representing knowledge is present in humans. [...] cognitive phenomena. In the first place, human cognition knowledge about a particular category is distributed is generative: in spite of the fact that human mind is across the modality-specific systems that process its presumably finite, we can conceive and understand an properties” (p. 309). Therefore, according to Barsalou, a) unlimited number of thoughts that we never encountered we can speak of a "conceptual system" also in the case of before. Moreover, also systematicity of cognition seems non human animals; b) also low-level forms of to depend on compositionality: the ability of conceiving categorisation, that depend on some specific perceptual certain contents is related in a systematic way to the modality pertain to the conceptual system. Elizabeth ability of conceiving other contents. For example, if Spelke’s experiments on infants (see e.g. Spelke 1994; somebody can understand the sentence the cat chases a Spelke and Kinzler 2007) are symptomatic of the rat, then she is presumably able to understand also a rat difference in approach between psychologists and chases the cat, in virtue of the fact that the forms of the philosophers. Such experiments demonstrate that some two sentences are syntactically related. We can conclude extremely general categories are very precocious and that the ability of understanding certain propositional presumably innate. According to the author, they show contents systematically depends on the compositional that newborn babies already possess certain concepts structure of the contents themselves. This can be easily (e.g., the concept of physical object). But some accounted for if we assume that mental representations philosophers interpreted these same data as a have a structure similar to a compositional language. paradigmatic example of the existence of nonconceptual contents in agents (babies) that had not yet developed a 2.2 Against "Classical" Concepts conceptual system. Compositionality is less important for many 2.1 Compositionality psychologists. In the field of psychology, most research on concepts moves from the critiques to the so-called The fact that philosophers consider concepts mainly as classical theory of concepts, i.e. the traditional point of the components of thoughts brought a great emphasis on view according to which concepts can be defined in terms compositionality, and on related features, such as of necessary and sufficient conditions. Rather, empirical productivity and systematicity, that are often ignored by evidence favours those approaches to concepts that accounts for prototypical effects. The central claim of the the philosophical and psychological points of view is highly classical theory of concepts (i.e.) is that every concept c schematic. 76 CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011 is defined in terms of a set of features (or conditions) f1, Moreover, things are made more complex by the ..., fn that are individually necessary and jointly sufficient fact that, also within the two fields of philosophy and psychology considered separately, the situation is not for the application of c. In other words, everything that very encouraging. In neither of the two disciplines does a satisfies features f1, ..., fn is a c, and if anything is a c, clear, unambiguous and coherent notion of concept seem then it must satisfy f1, ..., fn. For example, the features to emerge. Consider for example psychology. Different that define the concept bachelor could be human, male, positions and theories on the nature of concepts are adult and not married; the conditions defining square available (prototype view3, exemplar view, theory could be regular polygon and quadrilateral. This point of theory), that can hardly be integrated. From this point of view was unanimously and tacitly accepted by view the conclusions of Murphy (2002) are of great psychologists, philosophers and linguists until the middle significance, since in many respects this book reflects the of the 20th century. current status of empirical research on concepts. Murphy The first critique to the classical theory is due to a contrasts the approaches mentioned above in relation to philosopher: in a well known section from the different classes of problems, including learning, Philosophical Investigations, Ludwig Wittgenstein induction, lexical concepts and children’s concepts. His observes that it is impossible to individuate a set of conclusions are rather discouraging: the result of necessary and sufficient conditions to define a concept comparing the various approaches is that “there is no such as GAME (Wittgenstein, 1953, § 66). Therefore, clear, dominant winner” (ibid., p. 488) and that “[i]n concepts exist, which cannot be defined according to short, concepts are a mess” (p. 492). This situation classical theory, i.e. in terms of necessary and sufficient persuaded some scholars to doubt whether concepts conditions. Rather, concepts like GAME rest on a constitute a homogeneous phenomenon from the point of complex network of family resemblances. Wittgenstein view of a science of the mind (see e.g. Machery 2005 and introduces this notion in another passage in the 2009; Frixione 2007). Investigations: «I can think of no better expression to characterise these similarities than “family 3 Concept Representation in Artificial resemblances”; for the various resemblances between Intelligence members of a family: build, features, colour of eyes, gait, The situation sketched in the section above is in some temperament, etc. etc.» (ibid., § 67). sense reflected by the state of the art in AI and, more in Wittgenstein's considerations were corroborated general, in the field of computational modelling of by empirical psychological research: starting from the cognition. This research area seems often to hesitate seminal work by Eleanor Rosch, psychological between different (and hardly compatible) points of view. experiments showed that common-sense concepts do not In AI the representation of concepts is faced mainly obey to the requirement of the classical theory2: usually within the field of knowledge representation (KR). common-sense concepts cannot be defined in terms of Symbolic KR systems (KRs) are formalisms whose necessary and sufficient conditions (and even if for some structure is, in a wide sense, language-like. This usually concept such a definition is available, subjects do not use involves that KRs are assumed to be compositional. it in many cognitive tasks). Rather, concepts exhibit In a first phase of their development (historically prototypical effects: some members of a category are corresponding to the end of the 60s and to the 70s) many considered better instances than others. For example, a KRs oriented to conceptual representations tried to keep robin is considered a better example of the category of into account suggestions coming from psychological birds than, say, a penguin or an ostrich. More central research. Examples are early semantic networks and instances share certain typical features (e.g., the ability of frame systems. Frame and semantic networks were flying for birds, having fur for mammals) that, in general, originally proposed as alternatives to the use of logic in are not necessary neither sufficient conditions. KR. The notion of frame was developed by Marvin Prototypical effects are a well established Minsky (1975) as a solution to the problem of empirical phenomenon. However, the characterisation of representing structured knowledge in AI systems4. Both concepts in prototypical terms is difficult to reconcile frames and most semantic networks allowed the with the requirement of compositionality. According to a possibility to characterise concepts in terms of well known argument by Jerry Fodor (1981), prototypes prototypical information. are not compositional (and, since concepts in Fodor's However, such early KRs where usually opinion must be compositional, concepts cannot be characterised in a rather rough and imprecise way. They prototypes). In synthesis, Fodor's argument runs as follows: consider a concept like PET FISH. It results 3 from the composition of the concept PET and of the Note that the so-called prototype view does not coincide with concept FISH. But the prototype of PET FISH cannot the acknowledgement of prototypical effects: as said before, result from the composition of the prototypes of PET and prototypical effects are a well established phenomenon that all of FISH. For example, a typical PET is furry and warm, a psychological theories of concepts are bound to explain; the prototype view is a particular attempt to explain empirical facts typical FISH is greyish, but a typical PET FISH is not concerning concepts (including prototypical effects). On these furry and warm neither greyish. aspects see again Murphy 2002. 4 Many of the original articles describing these early KRs can 2 On the empirical inadequacy of the classical theory and on the be found in (Brachman & Levesque 1985), a collection of psychological theories of concepts see (Murphy 2002). classical papers of the field. 77 CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011 lacked a clear formal definition, and the study of their incompatible with prototypical effects. But such meta-theoretical properties was almost impossible. When approaches pose various theoretical and practical AI practitioners tried to provide a stronger formal difficulties, and many unsolved problems remain. foundation to concept oriented KRs, it turned out to be In this section we overview some recent proposal difficult to reconcile compositionality and prototypical of extending concept-oriented KRs, and in particular representations. As a consequence, they often choose to DLs, in order to represent non-classical concepts. sacrifice the latter. Recently different methods and techniques have In particular, this is the solution adopted in a class been adopted to represent non-classical concepts within of concept-oriented KRs which had (and still have) wide computational ontologies. They are based on extensions diffusion within AI, namely the class of formalisms that of DLs and of standard ontology languages such as stem from the so-called structured inheritance networks OWL. The different proposals that have been advanced and from the KL-ONE system (Brachman and Schmolze can be grouped in three main classes: a) fuzzy 1985). Such systems were subsequently called approaches, b) probabilistic and Bayesan approaches, c) terminological logics, and today are usually known as approaches based on non-monotonic formalisms. description logics (DLs) (Baader et al. 2002). a) Following this direction, for as the integration A standard inference mechanism for this kind of of fuzzy logics in DLs and in ontology oriented networks is inheritance. Representation of prototypical formalisms, see for example Gao and Liu 2005, and information in semantic networks usually takes the form Calegari and Ciucci 2007, Stoilos et al. (2005) propose a of allowing exceptions to inheritance. Networks in this fuzzy extension of OWL, f-OWL, able to capture tradition do not admit exceptions to inheritance, and imprecise and vague knowledge, and a fuzzy reasoning therefore do not allow the representation of prototypical engine that lets f-OWL reason about such knowledge. information. Indeed, representations of exceptions can be Bobillo and Staccia (2009) propose a fuzzy extension of hardly accommodated with other types of inference OWL 2 for representating vague information in semantic defined on these formalisms, concept classification in the web languages. However, it is well known (Osherson and first place (Brachman 1985). Since the representation of Smith 1981) that approaches to prototypical effects based prototypical information is not allowed, inferential on fuzzy logic encounter some difficulty with mechanisms defined on these networks (e.g. inheritance) compositionality. can be traced back to classical logical inferences. b) The literature offers also several probabilistic In more recent years, representation systems in generalizations of web ontology languages. Many of this tradition have been directly formulated as logical these approaches, as pointed out in Lukasiewicz and formalisms (the above mentioned description logics, Straccia (2008), focus on combining the OWL language Baader et al., 2002), in which Tarskian, compositional with probabilistic formalisms based on Bayesian semantics is straightly associated to the syntax of the networks. In particular, Da Costa and Laskey (2006) language. Logical formalisms are paradigmatic examples suggest a probabilistic generalization of OWL, called PR- of compositional representation systems. As a OWL, whose probabilistic semantics is based on multi- consequence, this kind of systems fully satisfy the entity Bayesian networks (MEBNs); Ding et al. (2006) requirement of compositionality. This has been achieved propose a probabilistic generalization of OWL, called at the cost of not allowing exceptions to inheritance. By Bayes-OWL, which is based on standard Bayesian doing this we gave up the possibility of representing networks. Bayes-OWL provides a set of rules and concepts in prototypical terms. From this point of view, procedures for the direct translation of an OWL ontology such formalisms can be seen as a revival of the classical into a Bayesian network. A problem here could be theory of concepts, in spite of its empirical inadequacy in represented by the “translation” from one form of dealing with most common-sense concepts. “semantics” (OWL based) to another one. Nowadays, DLs are widely adopted within many c) The role of non-monotonic reasoning in the application fields, in particular within the field of the context of formalisms for the ontologies is actually a representation of ontologies. For example, the OWL debated problem. According to many KR researches, (Web Ontology Language) system5 is a formalism in this non-monotonic logics are expected to play an important tradition that has been endorsed by the World Wide Web role for the improvement of the reasoning capabilities of Consortium for the development of the semantic web. ontologies and of the Semantic Web applications. In the field of non-monotonic extensions of DLs, Baader and 4 Non-classical concepts in computational Hollunder (1995) propose an extension of ALCF system ontologies based on Reiter’s default logic6. The same authors, however, point out both the semantic and computational Of course, within symbolic, logic oriented KR, rigorous difficulties of this integration and, for this reason, approaches exist, that allow to represent exceptions, and propose a restricted semantics for open default theories, that therefore would be, at least in principle, suitable for representing “non-classical” concepts. Examples are 6 The authors pointed out that “Reiter's default rule approach fuzzy logics and non-monotonic formalisms. Therefore, seems to fit well into the philosophy of terminological systems the adoption of logic oriented semantics is not necessarily because most of them already provide their users with a form of ‘monotonic’ rules. These rules can be considered as special default rules where the justifications - which make the behavior 5 http://www.w3.org/TR/owl-features/ of default rules nonmonotonic – are absent”. 78 CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011 in which default rules are only applied to individuals monotonic “machine” reasoning for Semantic Web) can explicitly represented in the knowledge base. Because of be maybe adopted for local uses only or for specific Reiter’s default logic does not provide a direct of applications because it is “unsafe on the web”. Anyway, modelling inheritance with exceptions, Straccia (1993) the question about which “logics” must be used in the proposes an extension of DL H-logics (Hybrid KL-ONE Semantic Web (or, at least, until which degree, and in style logics) able to perform default inheritance which cases, certain logics could be useful) is still open. reasoning (a kind of default reasoning specifically The empirical results from cognitive psychology oriented to reasoning on taxonomies). This proposal is show that most common-sense concepts cannot be based on the definition of a priority order between default characterised in terms of necessary/sufficient conditions. rules. Donini et al. (1998, 2002), propose an extension of Classical, monotonic DLs seem to capture the DL with two non-monotonic epistemic operators. This compositional aspects of conceptual knowledge, but are extension allows one to encode Reiter’s default logic as inadequate to represent prototypical knowledge. But a well as to express epistemic concepts and procedural “non classical” alternative, a general DL able to represent rules. However, this extension presents a rather concepts in prototypical terms does not still emerge. complicated semantics, so that the integration with the As a possible way out, we sketch a tentative existing systems requires significant changes to the proposal that is based on some suggestions coming from standard semantics of DLs. Bonatti et al. (2006) propose cognitive science. Some recent trends of psychological an extension of DLs with circumscription. One of research favour the hypothesis that reasoning is not an motivating applications of circumscription is indeed to unitary cognitive phenomenon. At the same time, express prototypical properties with exceptions, and this empirical data on concepts seem to suggest that is done by introducing “abnormality” predicates, whose prototypical effects could stem from different extension is minimized. Giordano et al. (2007) propose representation mechanisms. In this spirit, we individuate an approach to defeasible inheritance based on the some hints that, in our opinion, could be useful for the introduction in the ALC DL of a typicality operator T7, development of artificial representation systems, namely: which allows to reason about prototypical properties and (i) the distinction between two different types of inheritance with exceptions. This approach, given the reasoning processes, which has been developed within nonmonotonic character of the T operator, encounters the the context of the so-called “dual process” accounts of problem of irrelevance (have some difficulties in the reasoning (sect. 5.1 below); (ii) the proposal to keep management of additional information that could be prototypical effects separate from compositional irrelevant for the reasoning). Katz and Parsia argue that representation of concepts (sect. 5.2); and (iii) the ALCK, a non monotonic DL extended with the epistemic possibility to develop hybrid, prototype and exemplar- operator K8 (that can be applied to concepts or roles) based representations of concepts (sect. 5.3). could represent a model for a similar non monotonic extension of OWL. In fact, according to the authors, it 5.1 A “dual process” approach would be possible to create “local” closed-world assumption conditions, in order the reap the benefits of Cognitive research about concepts seems to suggest that nonmonotonicity without giving up OWL’s open-world concept representation does not constitute an unitary semantics in general. phenomenon from the cognitive point of view. In this A different approach, investigated by Klinov and perspective, a possible solution should be inspired by the Parsia (2008), is based on the use of the OWL 2 experimental results of empirical psychology, in annotation properties (APs) in order to represent vague or particular by the so-called dual process theories of prototypical, information. The limit of this approach is reasoning and rationality (Stanovich and West 2000, that APs are not taken into account by the reasoner, and Evan and Frankish 2008). In such theories, the existence therefore have no effect on the inferential behaviour of of two different types of cognitive systems is assumed. the system (Bobillo and Straccia 2009). The systems of the first type (type 1) are phylogenetically older, unconscious, automatic, associative, parallel and 5 Some Suggestions from Cognitive Science fast. The systems of the type 2 are more recent, conscious, sequential and slow, and are based on explicit Though the presence of a relevant field of research, there rule following. In our opinion, there are good prima facie isn’t, in the scientific community, a common view about reasons to believe that, in human subjects, classification, the use of non-monotonic and, more in general, non- a monotonic form of reasoning which is defined on classical logics in ontologies. For practical applications, semantic networks, and which is typical of DL systems, systems that are based on classical Tarskian semantics is a task of the type 2 (it is a difficult, slow, sequential and that do not allow for exceptions (as it is the case of task). On the contrary, exceptions play an important role “traditional” DLs), are usually still preferred. Some in processes such as categorization and inheritance, researchers, as, for example, Pat Hayes (2001), argue that which are more likely to be tasks of the type 1: they are the non monotonic logics (and, therefore, the non fast, automatic, usually do not require particular conscious effort, and so on. 7 For any concept C, T(C) are the instances of C that are Therefore, a reasonable hypothesis is that a considered as “typical” or “normal”. concept representation system should include different 8 The K operator could be encoded in RDF/XML syntax of “modules”: a monotonic module of type 2, involved in OWL as property or as annotation property. 79 CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011 classification and in similar “difficult” tasks, and a non- the notion of concept is spurious from the cognitive point monotonic module involved in the management of of view. Both the compositional and the prototypical exceptions. This last module should be a "weak" non components contribute to the “conceptual behaviour” of monotonic system, able to perform only some simple the system (i.e., they have some role in those abilities that forms of non monotonic inferences (mainly related to we usually describe in terms of possession of concepts). categorization and to exceptions inheritance). This iii. According to Fodor, the majority of concepts solution goes in the direction of a “dual” representation are atomic. In particular, he claims that almost all of concepts within the ontologies, and the realization of concepts that correspond to lexical entries have no hybrid reasoning systems (monotonic and non structure. We maintain that many lexical concepts, even monotonic) on semantic network knowledge bases. though not definable in the terms classical theory, should exhibit some form of structure, and that such structure 5.2 A “Pseudo-Fodorian” proposal can be represented, for example, by means of a DL taxonomy. As seen before (section 2.2), according to Fodor, concepts cannot be prototypical representations, since 5.3 Prototypes and individuals concepts must be compositional, and prototypes do not compose. On the other hand, in virtue of the criticisms to As we told before (section 2.2), within the field of “classical” theory, concepts cannot be definitions. psychology, different positions and theories on the nature Therefore, Fodor argues that (most) concepts are atoms, of concepts are available. Usually, they are grouped in i.e., are symbols with no internal structure. Their content three main classes, namely prototype views, exemplar is determined by their relation to the world, and not by views and theory-theories (see e.g. Murphy 2002, their internal structure and/or by their relations with other Machery 2009). All of them are assumed to account for concepts (Fodor 1987, 1998). Of course, Fodor (some aspects of) prototypical effects in acknowledges the existence of prototypical effects. conceptualisation. However, he claims that prototypical representations are According to the prototype view, knowledge about not part of concepts. Prototypical representations allow to categories is stored in terms of prototypes, i.e. in terms of individuate the reference of concepts, but they must not some representation of the “best” instances of the be identified with concepts. Consider for example the category. For example, the concept CAT should coincide concept DOG. Of course, in our minds there is some with a representation of a prototypical cat. In the simpler prototypical representation associated to DOG (e.g., that versions of this approach, prototypes are represented as dogs usually have fur, that they typically bark, and so (possibly weighted) lists of features. on). But this representation does not the coincide with the According to the exemplar view, a given category concept DOG: DOG is an atomic, unstructured symbol. is mentally represented as set of specific exemplars We borrow from Fodor the hypothesis that explicitly stored within memory: the mental compositional representations and prototypical effects are representation of the concept CAT is the set of the demanded to different components of the representational representations of (some of) the cats we encountered architecture. We assume that there is a compositional during our lifetime. component of representations, which admits no Theory-theories approaches adopt some form of exceptions and exhibits no prototypical effects, and holistic point of view about concepts. According to some which can be represented, for example, in the terms of versions of the theory-theories, concepts are analogous to some classical DL knowledge base. In addition, a theoretical terms in a scientific theory. For example, the prototypical representation of categories is responsible concept CAT is individuated by the role it plays in our for such processes as categorisation, but it does not affect mental theory of zoology. In other version of the the inferential behaviour of the compositional approach, concepts themselves are identified with micro- component. theories of some sort. For example, the concept CAT It must be noted that our present proposal is not should be identified with a mentally represented micro- entirely “Fodorian”, at least in the following three senses: theory about cats. i. We leave aside the problem of the nature of These approaches turned out to be not mutually semantic content of conceptual representations. Fodor exclusive. Rather, they seem to succeed in explaining endorses a causal, informational theory of meaning, different classes of cognitive phenomena, and many according to which the content of concepts is constituted researchers hold that all of them are needed to explain by some nomic mind-world relation. We are in no way psychological data. In this perspsective, we propose to committed with such an account of semantic content. (In integrate some of them in computational representations any case, the philosophical problem of the nature of the of concepts. More precisely, we try to combine a intentional content of representations is largely irrelevant prototypical and an exemplar based representation in to our present purposes). order to account for category representation and ii. Fodor claims that concepts are compositional, prototypical effects (for a similar, hybrid prototypical and and that prototypical representations, in being not exemplar based proposal, see Gagliardi 2008). We do not compositional, cannot be concepts. We do not take take into consideration the theory-theory approach, since position on which part of the system we propose must be it is in some sense more vaguely defined if compared the considered as truly “conceptual”. Rather, in our opinion other two points of view. As a consequence, its 80 CEUR Proceedings 4th Workshop HCP Human Centered Processes, February 10-11, 2011 computational treatment seems at present to be less feasible. References 6. Concluding Remarks: Some Suggestion for Implementation Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P., 2003. The Description Logic In the field of web ontology languages, the Handbook: Theory, Implementations and developments sketched above appear nowadays, Applications. Cambridge University Press. technologically possible. Within the Semantic Web Baader, F., Hollunder, B., 1995. 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