Prototypes Vs Exemplars in Concept Representation

Marcello Frixione

and Antonio Lieto

DAFIST, University of Genova, Genoa, Italy

Computer Science Department, University of Turin, Turin, Italy

Keywords: Concept Representation, Formal Ontologies, Non Classical Concepts, Psychological Theories of Concepts,

Typicality Effects, Conceptual Spaces.

Abstract: Concept representation is still an open problem in the field of ontology engineering and, more in general, of

knowledge representation. In particular, it still remains unsolved the problem of representing "non classical"

concepts, i.e. concepts that cannot be defined in terms of necessary and sufficient conditions. In this paper

we review empirical evidence from cognitive psychology, which suggests that concept representation is not

an unitary phenomenon. In particular, it seems that human beings employ both prototype and exemplar

based representations in order to represent non classical concepts. We suggest that a similar, hybrid

prototype-exemplar based approach could be useful also in the field of formal ontology technology.

1 INTRODUCTION

This article deals with the problem of representing

non classical concepts in formal ontologies. By non

classical concepts we mean concepts that cannot be

represented in terms of sets of necessary and/or

sufficient conditions. After introducing the problem

(sect. 2), we review some empirical evidence from

cognitive psychology, which suggests that concept

representation is not an unitary phenomenon (sect.

3). In particular, prototype and exemplar based

models of non classical concepts are both plausible,

and can account for different aspects of human

abilities. In sect. 4 we argue that these results could

suggest the adoption of a hybrid approach in the

field of formal ontologies; in sect. 5 we sketch the

proposal of an architecture for concept

representation based on both prototypes and

exemplars. Some concluding remarks follow (sect.

6).

2 REPRESENTING NON

CLASSICAL CONCEPTS

The representation of common sense concepts is still

an open problem in ontology engineering and, more

in general, in Knowledge Representation (KR) (see

e.g. Frixione and Lieto, in press). Cognitive Science

showed the empirical inadequacy of the so-called

“classical” theory of concepts, according to which

concepts should be defined in terms of sets of

necessary and sufficient conditions. Rather, Eleanor

Rosch’s experiments (Rosch, 1975) – historically

preceded by the philosophical analyses by Ludwig

Wittgenstein (Wittgenstein, 1953) – showed that

ordinary concepts can be characterized in terms of

prototypical information.

These results influenced the early researches in

knowledge representation: the KR practitioners

initially tried to keep into account the suggestions

coming from cognitive psychology, and designed

artificial systems – such as frames and early

semantic networks – able to represent concepts in

“non classical” (prototypical) terms (for early KR

developments, see Brachman and Levesque, 1985).

However, these early systems lacked clear

formal semantics and a satisfactory meta-theoretic

account, and were later sacrificed in favour of a

class of formalisms stemmed from the so-called

structured inheritance semantic networks and the

KL-ONE system (Brachman and Schmoltze, 1985).

These formalisms are known today as description

logics (DLs, Baader et al., 2010). DLs are logical

formalisms, which can be studied by means of

traditional, rigorous metatheoretic techniques

developed by logicians. However, they do not allow

exceptions to inheritance, and the possibility to

represent concepts in prototypical terms. From this

point of view, therefore, such formalisms can be

seen as a revival of the classical theory of concepts.

226

Frixione M. and Lieto A..

Prototypes Vs Exemplars in Concept Representation.

DOI: 10.5220/0004139102260232

In Proceedings of the International Conference on Knowledge Engineering and Ontology Development (KEOD-2012), pages 226-232

ISBN: 978-989-8565-30-3

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

As far as prototypical information is concerned, such

formalisms offer only two possibilities: representing

it resorting to tricks or ad hoc solutions, or,

alternatively, ignoring it. For obvious reasons, the

first solution in unsuitable: it could have disastrous

consequences for the soundness of the knowledge

base and for the performances of the entire system.

The second choice severely reduces the expressive

power of the representation. For example, in

information retrieval terms, this could severely

affect the system's recall. Let us suppose that you are

interested in documents about flying animals. A

document about birds is likely to interest you,

because most birds are able to fly. However, flying

is not a necessary condition to being a bird (there are

many birds that are unable to fly). So, the fact that

birds usually fly cannot be represented in a

formalism that allows only the representation of

concepts in classical terms, and the documents about

birds will be ignored by your query.

Nowadays, DLs are widely adopted within many

fields of application, in particular within the area of

ontology representation. For example, OWL is a

formalism in this tradition, which has been endorsed

by the World Wide Web Consortium for the

development of the Semantic Web. However, DL

formalisms leave unsolved the problems of

representing concepts in prototypical terms.

Within the field of logic oriented KR, rigorous

approaches exist, designed to make it possible the

representation of exceptions, and that therefore are,

at least in principle, suitable for dealing with (some

aspects of) “non-classical” concepts. Examples are

fuzzy and non-monotonic logics. Therefore, the

adoption of logic oriented semantics is not

necessarily incompatible with the representation of

prototypical effects. Various fuzzy and non-

monotonic extensions of DL formalisms have been

proposed. Nevertheless, such approaches pose

various theoretical and practical problems, which in

part remain unsolved (see Frixione and Lieto, 2010

for a discussion).

As a possible way out, we outline here a tentative

proposal that goes in a different direction, and that is

based on some suggestions coming from empirical

cognitive science research. Within the field of

cognitive psychology, different positions and

theories on the nature of concepts are available; all

of them are assumed to account for (some aspects

of) prototypical effects in conceptualisation (see e.g.

Murphy, 2002 and Machery, 2009). Here we shall

take into account two of such approaches, namely

prototypes and the so-called exemplar view.

According to the prototype view, knowledge

about categories is stored in terms of prototypes, i.e.

in terms of some representation of the “best”

instances of the category. For example, the concept

CAT should coincide with a representation of a

prototypical cat. In the simpler versions of this

approach, prototypes are represented as (possibly

weighted) lists of features.

According to the exemplar view, a given

category is mentally represented as set of specific

exemplars explicitly stored within memory: the

mental representation of the concept CAT is the set

of the representations of (some of) the cats we

encountered during our lifetime.

These approaches turned out to be not mutually

exclusive. Rather, they seem to succeed in

explaining different classes of cognitive phenomena,

and many researchers hold that all of them are

needed to explain psychological data (see again

Murphy, 2002 and Machery, 2009). In this

perspective, we propose to integrate some of them in

computational representations of concepts.

Prototype and exemplar based approaches to

concept representation are, as mentioned above, not

mutually exclusive, and they succeed in explaining

different phenomena. Exemplar based

representations can be useful in many situations.

According to various experiments, it can happen that

instances of a concept that are rather dissimilar from

the prototype, but are very close to a known

exemplar, are categorized quickly and with high

confidence. For example, a penguin is rather

dissimilar from the prototype of BIRD. However, if

we already know an exemplar of penguin, and if we

know that it is an instance of BIRD, it is easier for us

to classify a new penguin as a BIRD. This is

particularly relevant for concepts (such as

FURNITURE, or VEHICLE) whose members differ

significantly from one another.

Exemplar based representations are easier and

faster to acquire, when compared to prototypes. In

some situations, it can happen that there is not

enough time to extract a prototype from the

available information. Moreover, the exemplar based

approach makes the acquisition of concepts that are

not linearly separable easier (see Medin and

Schwanenflugel, 1981). In the following section we

shall review some of the available empirical

evidence concerning prototype and exemplar based

approaches to concept representation in psychology.

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227

3 EXEMPLARS VS.

PROTOTYPES IN COGNITIVE

PSYCHOLOGY

As anticipated in the previous section, according to

the experimental evidence, exemplar models are in

many cases more successful than prototypes.

Consider the so-called “old-items advantage effect”.

It consists in the fact that already known items are

usually more easily categorized than new items that

are equally typical (see Smith and Minda, 1998 for a

review). For example: it is easier for me to classify

my old pet Fido as a dog (even supposing that he is

strongly atypical) than an unknown dog with the

same degree of typicality. This effect is not

predicted by prototype theories. Prototype

approaches assume that people abstract a prototype

from the stimuli presented during the learning phase,

and categorize old as well as new stimuli by

comparing them to it. What matters for

categorization is the typicality degree of the items,

not whether they are already known or not. By

contrast, the old-item advantage is banal to explain

in the terms of the exemplar paradigm.

This is correlated to a further kind of empirical

evidence in favour of exemplar theories. It can

happen that a less typical item can be categorized

more quickly and more accurately than a more

typical category member if it is similar to previously

encountered exemplars of the category (Medin and

Schaffer, 1978). Consider the penguin example

mentioned in the previous section: a penguin is a

rather atypical bird. However, let us suppose that

some exemplar of penguin is already stored in my

memory as an instance of the concept BIRD. In this

case, it can happen that I classify new penguins as

birds more quickly and more confidently than less

atypical birds (such as, say, toucans or

hummingbirds) that I never encountered before.

Linearly separable

categories

Figure 1: Linearly separable and non separable categories.

Another important source of evidence for the

exemplar model stems from the study of linear

separable categories (see, again, Medin and

Schwanenflugel, 1981). Two categories are linearly

separable if and only if it is possible to determine to

which of them an item belongs by summing the

evidence concerning each attribute of this item. For

example, let us suppose that two categories are

characterized by two attributes, or dimensions,

corresponding to the axes in fig. 1. These categories

are linearly separable if and only if the category

membership of each item can be determined by

summing its value along the x and y axes, or, in

other terms, if a line can be drawn, which separates

the members of the categories.

According to the prototype approach, people

should find it more difficult to form a concept of a

non-linearly separable category. Subjects should be

faster at learning two categories that are linearly

separable. However, Medin and Schwanenflugel

(1981) experimentally proved that categories that are

not linearly separable are not necessarily harder to

learn. This is not a problem for exemplar based

theories, which do not predict that subjects would be

better at learning linearly separable categories. In the

psychological literature, this result has been

considered as a strong piece of evidence in favour of

the exemplar models of concept learning.

The above mentioned results seem to favour

exemplars against prototypes. However, other data

do not confirm this conclusion. Moreover, it has

been argued that many experiments favourable to the

exemplar approach rest on a limited type of

evidence, because in various experimental tasks a

very similar category structure has been employed

(Smith and Minda, 2000). Nowadays, it is

commonly accepted that prototype and exemplars

are not competing, mutually exclusive alternatives.

In fact, these two hypotheses can collaborate in

explaining different aspects of human conceptual

abilities (see e.g. Murphy, 2002 and Machery,

2009).

An empirical research supporting the hypothesis

of a multiple mental representation of categories is

in Malt (1989). This study was aimed to establish if

people categorize and learn categories using

exemplars or prototypes. The empirical data,

consisting in behavioral measures such as

categorization probability and reaction time, suggest

that subjects use different strategies to categorize.

Some use exemplars, a few rely on prototypes, and

others appeal to both exemplars and prototypes. A

protocol analysis of subjects’ descriptions of the

adopted categorization strategy confirms this

interpretation (a protocol analysis consists in

recording what the subjects of an experiment say

after the experiment about the way in which they

performed the assigned tasks). Malt (1989) writes:

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"Three said they used only general features of

the category in classifying the new exemplars. Nine

said they used only similarity to old exemplars, and

eight said that they used a mixture of category

features and similarity to old exemplars. If reports

accurately reflect the strategies used, then the data

are composed of responses involving several

different decision processes” (p. 546-547).

These findings are consistent with other well

known studies, such as Smith et al. (1997) and Smith

and Minda (1998). Smith et al. (1997) found that the

performances of half of the subjects of their

experiments best fitted the prototype hypothesis,

while the performances of the other half were best

explained by an exemplar model. Therefore, it is

plausible that people can learn at least two different

types of representation for concepts, and that they

can follow at least two different strategies of

categorization. Smith and Minda (1998) replicated

these findings and, additionally, found that during

the learning, subjects’ performances are best fitted

by different models according to the features of the

category (e.g., its dimensions) and the phase of the

learning process, suggesting that when learning to

categorize artificial stimuli, subjects can switch from

a strategy involving prototypes to a strategy

involving exemplars. They also found that the

learning path is influenced by the properties of the

learned categories. For example, categories with

few, dissimilar members favour the use of exemplar-

based categorization strategies. Thus, psychological

evidence suggests that, in different cases, we employ

different categorization mechanisms.

Summing up, prototype and exemplar

approaches present significant differences, and have

different merits. We conclude this section with a

brief summary of such differences. First of all,

exemplar-based models assume that the same

representations are involved in such different tasks

as identification (e.g., “this is the Tower Bridge”)

and categorization (Nosofsky, 1986). This contrasts

with prototype models, which assumes that these

tasks involve different kinds of representations.

Furthermore, prototype representations synthetically

capture only some central, and cognitively relevant,

aspects of a category, while models based on

exemplars are more analytical, and represent in toto

the available knowledge concerning the instances of

a given category.

This is related to another aspect of divergence,

which pertains the categorization process. Both

prototype and exemplar models assume that the

similarity between prototypical/exemplar

representations and target representations is

computed. The decision of whether the target

belongs to some category depends on the result of

this comparison. However, important differences

exist. According to the prototype view, the

computation of similarity is usually assumed to be

linear. Indeed, since prototypes are synthetic

representations, all information stored in them is

relevant. Therefore, if some property is shared by

the target and by some prototype, this is sufficient to

increase the similarity between them, independently

from the fact that other properties are shared or not.

On the contrary, an exemplar based representation

includes information that is not relevant from this

point of view (typically, information that

idiosyncratically concerns specific individuals). As a

consequence, the computation of similarity is

assumed to be non-linear: an attribute that is shared

by the target and by some exemplar is considered to

be relevant only if other properties are also shared.

Prototypes and exemplar based approaches

involve also different assumptions concerning

processing and memory costs. According to the

exemplar models, a category is mentally represented

by storing in our long term memory many

representations of category members; according to

prototype theorists, only some parameters are stored,

which summarize the features of a typical

representative of the category. As a consequence, on

the one hand, prototypes are synthetic

representations that occupy a smaller memory space.

On the other hand, the process of creating a

prototype requires more time and computational

effort if compared to the mere storage of knowledge

about exemplars, which is computationally more

parsimonious, since no abstraction is needed.

4 HYBRID

PROTOTYPE-EXEMPLAR

REPRESENTATIONS

Given the evidence presented in the above section, it

is likely, in our opinion, that a dual, prototype and

exemplar based, representation of concepts could

turn out to be useful for the representation of non

classical concepts in ontological knowledge bases

also from a technological point of view.

In the first place, there are kinds of concepts that

seem to be more suited to be represented in terms of

exemplars, and concepts that seem to be more suited

to be represented in terms of prototypes. For

example, in the case of concepts with a small

number of instances, which are very different from

one another, a representation in terms of exemplars

PrototypesVsExemplarsinConceptRepresentation

229

should be more convenient. An exemplar based

representation could be more suitable also for non

linearly separable concepts (see the previous

section).

On the other hand, for concepts with a large

number of very similar instances, a representation

based on prototypes seems to be more appropriate.

Consider for example an artificial system that deals

with apples (for example a fruit picking robot, or a

system for the management of a fruit and vegetable

market). Since it is no likely that a definition based

on necessary/sufficient conditions is available or

adequate for the concept APPLE, then the system

must incorporate some form of representation that

exhibits typicality effects. But probably an exemplar

based representation is not convenient in this case:

the systems has to do with thousands of apples,

which are all very similar one another. A prototype

would be a much more natural solution.

In many cases, the presence of both a prototype

and an exemplar based representation seems to be

appropriate. Let us consider the concept BIRD. And

let us suppose that a certain number of individuals

, …., b

are known by the systems to be instances

of BIRD (i.e., the system knows for sure that b

, ….,

are birds). Let us suppose also that one of these

's (say, b

) is a penguin.

Then, a prototype P

BIRD

is extracted from

exemplars b

, …., b

, and it is associated with the

concept BIRD. Exemplar b

concurs to the

extraction of the prototype, but, since penguins are

rather atypical birds, it will result to be rather

dissimilar from P

BIRD

. Let us suppose now that a

new exemplar b

of penguin must be categorized. If

the categorization process were based only on the

comparison between the target and the prototype,

then b

(which in its turn is rather dissimilar from

BIRD

) would be categorized as a bird only with a

low degree of confidence, in spite of the fact that

penguins are birds in all respects. On the other hand,

let us suppose that the process of categorization

takes advantage also of a comparison with known

exemplars. In this case, b

, due to its high degree of

similarity to b

, will be categorized as a bird with

full confidence. Therefore, even if a prototype for a

given concept is available, knowledge of specific

exemplars should be valuable in many tasks

involving conceptual knowledge. On the other hand,

the prototype should be useful in many other

situations.

5 A HYBRID

PROTOTYPE-EXEMPLAR

ARCHITECTURE

In this section we outline the proposal of a possible

architecture for concept representation, which takes

advantage of the suggestions presented in the

sections above. It is based on a hybrid approach, and

combines a component based on a Description Logic

(DL) with a further component that implements

prototypical representations.

Concepts in the DL component are represented

as in fig. 2. As usual, every concept can be

subsumed by a certain number of superconcepts, and

it can be characterised by means of a number of

attributes, which relate it to other concepts in the

knowledge base. Restrictions on the number of

possible fillers can be associated to each attribute.

Given a concept, its attributes and its

concept/superconcept relations express necessary

conditions for it. DL formalisms make it possible to

specify which of these necessary conditions also

count as sufficient conditions.

Since in this component only

necessary/sufficient condition can be expressed, here

concepts can be represented only in classical terms:

no exceptions and no prototypical effects are

allowed. Concepts can have any number of

individual instances, that are represented as

individual concepts in the taxonomy.

Figure 2: A concept in the DL component.

As an example, consider the fragment of network

shown in fig. 3.

Figure 3: An example of concept.

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Here the concept DOG is represented as a

subconcept of MAMMAL. Since DL networks can

express only necessary and/or sufficient conditions,

some details of the representation are very loose. For

example, according to fig. 3, a DOG may or may not

have a tail (this is the expressed by the number

restriction 0/1 imposed on the attribute has_tail),

and has an unspecified number of limbs (since some

dogs could have lost limbs, and teratological dogs

could have more than four legs). LASSIE and RIN

TIN TIN are represented as individual instances of

DOG (of course, concepts describing individual

instances can be further detailed, fully specifying for

example the values of the attributes inherited from

parent concepts).

Prototypes describing typical instances of

concepts are represented as data structures that are

external to the DL knowledge base. Such structures

could, for example, be lists of (possibly weighted)

attribute/value pairs that are linked to the

corresponding concept. Some attributes of the list

should correspond to attributes of the DL concept,

which value can be further specified at this level.

For example, the prototypical dog is described as

having a tail, and exactly four legs. Other attributes

of the prototype could have no counterpart in the

corresponding DL concept.

As far as the exemplar-based component of the

representations is concerned, exemplars are directly

represented in the DL knowledge base as instances

of concepts. (It may also happen that some

information concerning exemplars is represented

outside the DL component, in the form of Linked

Data. Typically, this could be the case of “non

symbolic” information, such as images, sounds,

etc.).

It must be noted that prototypical information

about concepts (either stored in the form of

prototypes or extracted from the representation of

exemplars) extends the information coded within the

DL formalism. The semantic network provides

necessary and/or sufficient conditions for the

application of concepts, as a consequence, such

conditions hold for every instance of concepts, and

cannot be violated by any specific exemplar. So,

what can be inferred on the basis of prototypical

knowledge can extend, but can in no way conflict

with what can be deduced from the DL based

component.

6 CONCLUSIONS

In conclusion, we assume that a hybrid

prototype/exemplar based representation of non

classical concepts could make ontological

representation of common-sense concepts more

flexible and realistic, thus avoiding at the same time

some frequent misuses of DL formalisms.

As a further development of the work presented

here, we are currently investigating the possibility of

adopting conceptual spaces (Gärdenfors, 2000) as an

adequate framework for representing both

prototypes and exemplars in many different

contexts. Gärdenfors (2004) and others (Adams and

Raubal, 2009) proposed conceptual spaces as a tool

for representing knowledge in the semantic web.

From our point of view, conceptual spaces could

offer a common, computational framework do

develop our proposal of representing concepts in

terms of both prototypes and exemplars.

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