=Paper=
{{Paper
|id=None
|storemode=property
|title=Representing concepts in artificial systems: a clash of requirements
|pdfUrl=https://ceur-ws.org/Vol-696/paper11.pdf
|volume=Vol-696
}}
==Representing concepts in artificial systems: a clash of requirements==
https://ceur-ws.org/Vol-696/paper11.pdf
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
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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.
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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.
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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”.
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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.
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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
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computational treatment seems at present to be less
feasible.
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