Representational Formats in Cognitive Semantics

Dirk Geeraerts

AbstractThe paper reviews the representational fortnals that are currently in use in Cognitive Semantics forthe diagrammatic representation of the semasiological structure of lexical items. Three major typesof representation will be distinguished: the radial set model popularized by Lakoff (1987), theschematic network model defined by Langacker (1987, 1991), and the overlapping sets modelintroduced by Geeraerts (1989b). It will be argued that (given a number of straightforward adapta-tions and additions), these three models are notational variants, in the sense that they exhibit thesame representational potentialities. This conclusion will be reached by examining whether thethree models can provide for the representation of four different types of data that arise from aprototype-theoretical conception of semantic structure. These four types of data are; salience ef-fects among readings, non-hierarchical semantics links among readings (like metaphor and meton-ymy), hierarchical semantic links among readings, and discrepancies between intuitive and analyti-cal definitions of polysemy.

1. Introductory Remarks

If Cognitive Semantics is defined as the type of semantic research conductedwithin the tradition of Cognitive Linguistics as represented by Langacker (1987,1991) and Lakoff (1987), then the introduction and elaboration of a prototype-theoretical conception of semantic stnicture constitutes a major contribution ofCognitive Semantics to the study of word meaning (cf. Taylor 1989); other con-tributions would include Lakoff's theory of generalized metaphors (Lakoff &Johnson 1980), Fillmore's frame semantics (1977, 1984), and Talmy's lexical-semantic typological research (1983, 1985), The present paper will review themost common representational formats currently used by Cognitive Semanticsresearchers for describing prototype-oriented semantic structures. These fomiatsinclude the radial set model popularized by Lakoff (1987), the schematic networkmodel defined by Langacker (1987, 1991), and the overlapping sets model intro-duced by Geeraerts (1989b). It will be argued that these three models are by andlarge notationally equivalent. Specifically, it will be shown that the three repre-

FoliaUnguisticaXXIX/1-2 0165-4004/95/29-21 S 2.-(C) Mouton de Gruyter, Berlin — Socieuis Liiif^iiisticd Euio/nwo

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sentational formats can (in some cases, with slight adaptations) deal adequatelywith various types of semantic data that crucially arise in the context of a proto-type-theoretical conception of semantic structure.

There are, to avoid possible misunderstandings, a number of things that thepaper will not do. The discussion is restricted to representations of semasiologicalstructures — roughly, the relationship between the various readings of lexicalitems. This implies that it is not primarily about onomasiological phenomena(although a comparison with lexical field representations will be given below),nor about representations of individual readings. The representational mecha-nisms developed by Langacker for dealing with phenomena like figure/grounddistinctions, for instance, will not be treated here, as they pertain to the distribu-tion of information within individual meanings rather than to the way in whichseveral such meanings are mutually related within the semantic structure of lexi-cal items.

Also, the paper does not deal with representation as a mechanism for storingand manipulating lexical information in formalized grammars, NLP programmes,or AI systems. Deliberately, the title mentions formats rather than formalisms:the formats meant here are primarily graphical ways of visually representinglexical-semantic analyses for expository purposes, not formal descriptions thatcan be automatically manipulated in the context of algorithmic rule systems. Thisis not to say that such fomialisms are undesirable or unattainable. Promisingattempts have been made, for instance, to model lexical-semantic prototype ef-fects in connectionist terms. The analysis of those representations is, however, atopic of its own that will be ignored altogether in the present paper.

It would be wrong to think, incidentally, that graphical representational for-mats are largely unrestricted in comparison with symbolic formalisms. The set ofbasic elements (lines, boxes, or whatever) chosen for a graphical representationcarries a symbolic meaning: boxes may be stipulated to represent sets, differenttypes of lines may be chosen to represent various kinds of relations, and so on.These choices determine how the representational elements may be combined,and restrict the kind of things that can be represented at all. The general questionasked in this paper may therefore be formulated as follows: do the representa-tional choices made in the radial set model, the schematic network model, and theoverlapping sets model restrict the representational possibilities of the threemodels in such a way that certain phenomena that are important in a prototype-theoretical conception of semantic structure could not be represented? Althoughthe three representational models as currently used highlight different phenomenafrom among the set of relevant facts, it will be shown that this is a restriction ofpractice rather than principle. All three models can be adapted and extended in

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such a way as to deal adequately with all the relevant phenomena that are heretaken as point of departure for the comparison.

2. Criteria for Evaluating Semasiological Representations

An investigation of the type intended here requires a set of criteria with which toevaluate the competing models. Such a set of criteria may take the form of anumber of data types that the different formats should be able to represent. Thesedata types in turn will derive from a theoretical model of semasiological struc-ture: what kind of phenomena can be expected to occur in the semantics of lexicalitems? Within a Cognitive Semantics framework, the latter question primarilyevokes the definition of prototypicality: what kinds of phenomena fall under theconceptual scope of the notion "prototypicality"?

In Geeraerts (1989a), it is argued that prototypicality effects fall into four, notnecessarily coinciding classes. The classification involves a distinction betweenflexibility (or, defined negatively, the absence of rigidity) and difterences ofstructural weight (or, negatively, the absence of equality) as structural character-istics of prototype-based categories. These two features may be identified on anintensional level (where definitional descriptions of a category are at stake) andon an extensional level (where the members of a category are envisaged). In thecontext of the present paper, however, we will be concerned primarily with theintensional side of the fourfold classification that results from the cross-classification of the two conceptual pairs just described. Such a restriction tointensional phenomena is not uncommon in lexical semantics, given that defini-tion is one of its major concerns. Moreover, the extensional aspect of the matterwill not be entirely neglected; it will become clear further on in the article, how-ever, that it can be easily incorporated into a representation that starts off on anintensional basis. To begin, then, let us have a closer look at the two crucial phe-nomena as defined from an intensional perspective.

2.7 Intensional non-rigidity

Intensional non-rigidity involves the absence of classical definitions for a cate-gory: if no definition in terms of necessary-and-sufficient attributes is availablefor a category, then that category is defined less rigidly than the classical modelof definitions predicts. Instead of a single description consisting of individuallynecessary and jointly sufficient features, the definition takes the fonn of a multi-plicity of partial descriptions.

However, as argued in Geeraerts (1987), the so-called absence of classicaldefinitions as such does not suffice to establish the non-orthodo.x. prototype-basednature of lexical categories. Even in the classical model, the absence of a single

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definition in terms of necessary and sufficient attributes is a regular feature oflexical categories — in those cases where they are polysemous, in fact: if apolysemous category is conceived of as one that cannot be adequately describedby means of a single definition, then it necessarily fits the description of inten-sional non-rigidity mentioned above. A solution for this conceptual problem re-quires making a distinction between various operational definitions of polysemy(for a more extensive treatment, see Geeraerts 1993). The absence of classicaldefinability, then, is only a non-orthodox feature of lexical categories if it relatesnot to the (polysemous) category as a whole, but rather to the individual readingswithin that polysemous set. This involves distinguishing between two ways ofdetermining what a distinct reading of a lexical item is.

On the one hand, a number of operational tests reveals what is, from an in-tuitive point of view, a different meaning of a lexical item. One of these tests isQuine's "p and not p" test (1960): taking into account the readings "harbour" and"fortified sweet wine from Portugal" of port, these readings are revealed as trulydifferent meanings (or "senses") by the possibility of uttering, in a specific con-text, a sentence like Sandeman is a port but not a port. If port were merelyvague rather than polysemous between the "harbour" and the "wine" reading,such a sentence would turn out to be invariably contradictory.

On the other hand, a definitional criterion for polysemy (as informally statedby Aristotle in the Posterior Analytics Il.xiii) says that an item has more than onelexical meaning if there is no minimally specific definition covering the extensionof the item as a whole, and that it has no more lexical meanings than there aremaximally general definitions necessary to describe its extension. Definitions oflexical items should be maximally general in the sense that they should cover aslarge a subset of the extension of an item as possible. Thus, separate definitionsfor "blended sweet fortified wine from Portugal" and "vintage sweet fortifiedwine from Portugal" could not be considered definitions of lexical meanings,because they can be brought together under the definition "sweet fortified winefrom Portugal" On the other hand, definitions should be minimally specific in thesense that they should be sufficient to distinguish the item from other non-synonymous items. A maximally general definition covering both port "harbour"and port "kind of wine" under the definition "thing, entity" is excluded because itdoes not capture the specificity ot port as distinct from other items.

Given these two approaches, it may now be shown that discrepancies be-tween both (and hence, non-traditional forms of semantic structure) may exist.On the one hand, word meanings that have to be recognized as single senses ac-cording to an intuitive approach, appear to lack a classical definition (i.e. wouldhave to be recognized as polysemous according to the definitional criterion). This

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is the case for the "biological species" reading of bird, as analyzed in figure 1:the reading "member of the biological species Aves" functions as a single mean-ing (a penguin is a bird but not a bird is decidedly odd), but there is no classicaldefinition complying with the necessity-cum-sufficiency criterion. (The featuresthat are common to all birds as indicated in figure 1 are not jointly distinctive, asthey also apply to the duck-billed platypus.) On the other hand, there exist caseswhere what is an intuitively distinct meaning is smaller than what would be rec-ognized as a separate sense according to the definitional approach. Examples areprovided by autohyponymous words like dog, which has both the general reading"member of the species Canis familiaris", and the restricted meaning "malemember of the species Canis familiaris" In the latter reading, dog is an antonymof bitch; in the former, it contrasts with other animal terms (like cat). Now, theset-theoretically more restricted meaning "male dog" does not have the generalitythat is required according to the definitional criterion (because the "male dog"cases can always be subsumed under the definition of the hyperonymous reading"Canis familaris in general, regardless of sex"), but at the same time, Mirza is adog but not a dog makes perfect sense, assuming that Mirza is a bitch.

Figure I: A definitional analysis of "bird"model

in an overlapping sets

O)as

e.g. robin e.g. ostrich

e.g. penguin ^

e.g.chicken

[̂

g

a. 'Being able to fly*

b. "Having feathers'

c. 'Being S-shaped"

d. 'Having wings'

a. "Not domesticated"

f. "Being born from eggs"

g. 'Having a beak or bili'

In short, what is at stake with regard to intensional non-rigidity as one of the fourtypes of prototypicality effects is not the absence of classical definability as such,but rather a discrepancy between intuitive and definitional conceptions ofpolysemy.

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2.2 Intensional non-equality

Intensional non-equality takes the form of differences in the structural importanceof the various subsets that may be definitionally distinguished within the range ofapplication of a lexical item. There is a deliberate vagueness in this formulation,to the extent that the "subsets" in question may either constitute different mean-ings in the traditional sense or not. If they do, the intensional differences ofstructural weight involve differences of salience among the various meanings of aword. Let us observe, for instance, that bird might be used metaphorically to in-dicate an airplane (as in a gigantic silver bird approached from the west). Thatmetaphorical extension from the "biological species" reading would certainly beless salient than the latter as such. This is true from a logical point of view (to theextent that the metaphorical reading is a semantic extension of the former), froma psychological point of (to the extent that the metaphorical reading is less likelyto be permanently stored in the mental lexicon of the language user), and from astatistical point of view (to the extent that the metaphorical reading is less com-mon than the literal one). Admittedly, it need not always be the case that the vari-ous indices of salience coincide as neatly as in the example, but at least it will beclear what criteria may be taken into account to establish salience.

If the differently weighted subsets do not constitute word meanings in thetraditional sense, they involve subsets of the kind found in figure 1. The defini-tional analysis of bird divides the range of application of that word (in its literalreading) into a number of subsets: we may, for instance, distinguish the centralsubset comprising robins and other usual birds from a peripheral subset such asthe one including ostriches. The centrality relationship between the sets as suchindicates the differences in salience: the central set includes typical birds. It maybe noted that there is a second way of defining subsets with regard to figure 1.Instead of talking about the minimal subsets distinguished in the figure (in thesense in which ostriches belong to a different subset than robins), maximal sub-sets may be envisaged (in the sense in which ostriches, robins, and chickens be-long to the subset defined by the feature "having feathers"). Minimal subsets inthe figure are defined in terms of multiple descriptive features, whereas maximalsubsets are based on single features. It is a traditional part of prototype-theoretical semantics, then, that the most salient minimal subset tends to coincidewith that area where a maximal number of maximal subsets overlap. Or, in otherwords, the prototypical instances of a category are those in which a maximalnumber of structurally relevant characteristics coincide.

Regardless of whether the intensional salience effects at stake here are situ-ated within or among different meanings, they invariably involve cases of struc-tured polysemy. The term polysemy is obviously somewhat confusing here, since

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it normally only relates to situations of the first type described above, i.e. thoseinvolving different meanings in the traditional sense. A more neutral term, en-compassing both situations, could be multiple semantic applicability, but as thatexpression introduces an unacceptable cumbersomeness, we may stick topolysemy for the present purposes. The polysemy is a structured one, because thedifferently weighted subsets are related among each other by means of specificstructural links. In the bird example, the subsets within the literal reading("member of the biological species Aves") are related by similarity: the periph-eral subsets are related by partial similarity to the central subset that includesrobins and the other regular birds. Further, the literal reading is related by ametaphorical link to the peripheral "airplane" reading. (It may be remarked thatmetaphor also involves relations of similarity, but the terminological point wouldthen be to distinguish literal from figurative similarity. In what follows, we willuse similarity to refer to literal similarity, and metaphor for figurative similarity.)Similarity and metaphor do not exhaust the set of possible relations in polyse-mous clusters as intended here. In general, all relations that have been tradition-ally identified in diachronic semantics may recur in the synchronic structure oflexical items; metonymical relations, for instance, can be expected to be veryfrequent.

One specific kind of semantic relationship deserves to be mentioned sepa-rately, as it plays a crucial role in one of the representational formats that we willbe dealing with in paragraph 3. In traditional diachronic semantics,"specialization" and "generalization" refer to hierarchical semantic relations, i.e.relations that can be situated along the vertical dimension of a taxonomical tree.The specialization/generalization relationship holds, for instance, between the"male Canis familiaris" reading of dog and its "Canis familiaris in general"reading. In extensional terms, the more specialized reading is always a propersubset of the more general reading. Other terms beside "specialization" and"generalization" are often used; "abstraction" and "schematization" in particularmay be met with as synonyms of "generalization" The importance of hierarchi-cal semantic relations in the classical definability debate will be obvious from thediscussion in section 2.1.: the ideal of classical definability implies that for anyintuitively distinct reading of an item, a distinctive definition can be found thatgeneralizes over the specific instances of use that fall within the range of thatreading.

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3. The Current Representational Formats

3.1 The overlapping sets model, the radial set model, and the schematic net-work model

The three representational models that are currently used in Cognitive Semanticsare the overlapping sets model, the radial set model, and the schematic networkmodel. The overlapping sets model is illustrated by figure 1; applications may befound in studies such as Geeraerts (1990), Cuyckens (1991), Schmid (1993),Geeraerts, Grondelaers & Bakema (1994). The basic elements in this representa-tional format are the members of a category (such as the types of birds in figure1), or, in some cases, instances of use of the category as found in a text corpus.These basic elements are grouped together on the basis of the features that theyshare or the senses that they exemplify. Each grouping is typographically repre-sented by means of a Venn-diagram. The different groupings may overlap; thearea in the figure where the sets overlap maximally constitutes the prototypicalcenter of the category.

Figure 2: A definitional analysis of "bird" in a radialset model

The radial set model is described in Lakoff (1987); examples may be found inthe work of Brugman (1989), Janda (1990), Nikifoddou (1991), Goldberg(1992), and others. The basic elements in a radial set representation are themeanings or senses of a category; these are connected in pairwise fashion bymeans of relational links that indicate how one reading is an extension of an an-other (for instance, on the basis of similarity). The typographical distribution of

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the various readings on the page illustrates the prototypical structure of the cate-gory: the prototypical sense is situated roughly in the middle of the figure, whilethe extensions that emanate from this central sense are grouped radially around it.In more complex figures, a sense from which many others emanate is likely to behighly salient within the category. Figure 2, which is adapted from Cuyckens(1991), shows how the overlapping sets representation of figure 1 can be trans-formed into a radial set representation. (Note that the features 1-7 in figure 2correspond to features a-g in figure 1.) Figure 2 is, however, not entirely canoni-cal as far as radial set representations go: the visual metaphor indicating the cen-tral position of the 1234567-case is not included (but this could, of course, beremedied by shifting the 1234567-case to the middle of the square formed by theother readings). Also, figure 2 differs from the usual radial set representations tothe extent that the elements of the radial set (types of birds) are referential sub-sets (or, if one wishes, members) of the category "bird", rather than meanings orsenses in the usual sense.

Figure 3: A definitional analysis of "bird" in aschematic network model

bird'

bird

/ \

^

N

Chicken

robin sparrow blackbird

The schematic network model is described in detail by Langacker (i 987, 1991);it is illustrated by the work of Rudzka-Ostyn (1985, 1989), Tuggy (1987, 1993),Taylor (1992), Casad (1992), Schuize (1993), and others. The basic elements inthe schematic network model may be meanings or members of a category. As inthe radial set model, these elements are connected by means of relational links,but a systematic distinction is maintained between two kinds of links: links ofschematization and links of extension. Schematicity involves the relationshipbetween a subordinate node and a superordinate node in a taxonomical hierarch>.

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The category "bird", for instance, is schematic with regard to "robin","sparrow", "ostrich", and other types of birds. Extension, on the other hand, in-volves partial schematicity: assuming that the subset comprising robins, spar-rows, blackbirds (and others) constitutes the prototypical center of the category"bird", the subset comprising chickens is an extension from that prototype.Chickens do not fall within the prototypical subset, but the concept "chicken" canbe seen as an extension (based on a relationship of similarity) of the prototypicalsense. (And the same holds, obviously, for "kiwi", "ostrich", and "penguin".)Precisely because the example involves similarity, the relation is one of partialschematicity. Typographically, the schematization links are indicated by solidarrows along the vertical dimension of the figure, whereas the extension links arerepresented by broken arrows along the horizontal dimension of the representa-tion. Prototypicality may be indicated by using thicker lines for drawing theboxes in the figures. Figure 3 represents part of the "bird"-category in the form ofa schematic network. (The concept BIRD' corresponds with the prototypical caseof figures 1 and 2; BIRD represents the category as a whole. The introduction of aBiRD'-node is necessary if a separate representation of the prototype of the cate-gory is required.)

3.2 Onomasiological parallels

An instructive parallel may be drawn between, on the one hand, the distinctionbetween radial set and schematic network representations versus an overlappingsets representation, and on the other hand, alternative representations pertainingto the structure of lexical fields. In the former case (the case that primarily inter-est us here), the representations involve the semasiological structure of individuallexical items — roughly, the relationship between the various readings of a lexi-cal item. In the latter case, the representations involve the onomasiologicalstructure of lexical fields — the semantic associations between various wordsthat are somehow related in meaning. (Note, incidentally, that the term onomasi-ology is used here in a broad sense, where it includes any association of lexicalitems on the basis of semantic relatedness. There also exists a more restrictedinterpretation of the term, in which it refers exclusively to alternative lexicaliza-tions of specific senses or referents.)

In lexical field research, then, three major types of representational formal-isms may be distinguished:

First, the traditional representation as found in, for instance, Lehrer (1974)takes the field metaphor more or less literally, by positioning the lexical items inthe field in a two-dimensional space. The distinction between the items may thenbe indicated by dividing the field on the basis of .semantic dimensions (that eachoccur with specific values). In the upper part of figure 4, an abstract example is

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presented with four items distinguished by two semantic dimensions (numbered 1and 2). Each dimension is a binary one, so that the dimensional values may beindicated by means of plus and minus signs.

The second representational format is the componential one popularized(though not invented) by Katz & Fodor (1963). A componential analysis turns thetwo-dimensional analysis inside out: the distinctive dimensions that structure thefield are now placed "within" the lexical items, as part of their definition. Byattributing a separate definition to each item in isolation, the associative linksamong the items remain implicit: they have to be derived from the presence orabsence of specific features in the componential definitions.

Finally (as exemplified in the lower part of figure 4), a relational representa-tion joins the traditional type in that it does not look inside the lexical items butpresents them as entities without internal structure linked by external relations.The distinction between the first type of representation and the present one re-sides in the nature of the links grouping together lexical items. The first approachdistinguishes sets of items on the basis of shared features like the dimensionalvalues -1-1 or -2; the sets overlap in the sense in which, for instance, item A be-longs both to the set defined by -i-l and to that defined by -\-2. In the relationalrepresentation, the groupings consist of individual links between pairs of lexicalitems; following the definition of the relational approach in Lyons (1963), therelations usually envisaged are taken from a restricted set including at least

Figure 4: Alternative representations of semantic relations in a lexical field

TRADITIONAL FIELD REPRESENTATION:

DIMENSIONAL

VALUE + 2

DIMENSIONAL

VALUE-2

DIMENSIONAL

VALUE-1-1

Item A

ItemC

DIMENSIONAL

VALUE-1

Item B

itemD

COMPONENTIAL ANALYSIS:

Item A Item B+] -1+2 +2

RELATIONAL NETWORK

Item C+ 1-2

Item-1-2

REPRESENTATION:

• r

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hyponymy, antonymy, and synonymy (but extensions of the set are not unusual,cf. Cruse 1986). In the example of figure 4, the opposite values of the items withregard to the dimensions 1 and 2 are interpreted as an antonymous relationship(in the sense in which antonyms like alive and dead might be componentiallyrepresented as H-LIVE versus -LIVE).

The semasiological representations compared in the present paper may nowbe aligned with the onomasiological ones just reviewed. On the one hand, theradial set representation and the schematic network representation are both rela-tional formats to the extent that they primarily link individual readings of lexicalitems in pairwise fashion. They are, in other words, network representations. Theoverlapping sets representation, on the other hand, is of the same "set-theoretical"kind as the first type distinguished in the case of lexical fields. The relations be-tween the approaches presented so far are schematically represented in figure 5.

Figure 5: The relationship between the semasiological and theonomasiological representational formats

SEMASIO-

LOGY

ONOMASIO-

LOGY

EXTERNALC

RELEVAKl

BINARY

RELATIONS

-radial sets-schematicnetworks

relationalapproach

ROUPING OF

r ENTITIES

OVERLAPPING

SETS

overlappingsets model

traditionalfield approach

INTERNAL

ANALYSIS OF

RELEVANT

ENTITIES

componentialanalysis

componentialanalysis

An important remark with regard to the schematic overview in figure 5 concernsthe presence of the componential approach on the semasiological level. First ofall, it should be noted that the componential approach in its Katzian form is al-ready both a semasiological and an onomasiological representational format: thestructural analysis of the lexical field automatically yields a definition of theitems in the field. Moreover, the componential approach need not take its starting-point in a lexical field, but may also start from the polysemous set of readingsattached to a single lexical item. One may compare, for instance, Pottier's field-based application of componential analysis (1964) with Katz & Fodor's word-based approach. Within the domain of Cognitive Semantics, radial set represen-

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tations have sometimes been enriched with componential descriptions of thenodes in the network; see, for instance, Brugman's analysis of over (1989), andthe example presented in figure 2, as drawn from Cuyckens (1991). As an overallrepresentation of semasiological data, however. Cognitive Semantics has tendedto avoid componential analysis (compare Fillmore 1975). The basic reason seemsto be that a componential analysis, describing various readings in isolation, tendsto obscure the structural relations among those word meanings. Specifically, theprototype-based differences of salience (or structural weight) that are crucial toCognitive Semantics are not automatically incorporated into a componential rep-resentation.

4. Current Formats as Notational Variants

The representational formats of paragraph 3 may now be compared among eachother on the basis of the requirements formulated in paragraph 2. We will indicatehow each of the three representations in their usual form deals with the varioustypes of information discussed in section 2. It will be shown that they are, by andlarge, notational variants.

Differences of salience among subsets in the range of application of an itemare represented in roughly the same ways in the three models. On the one hand,salience effects receive an indirect, structural representation. In the overlappingsets model, for instance, salient subsets are those that are constituted by multipleoverlapping, i.e. by the coincidence of a large number of relevant descriptivefeatures. Similarly, in the radial set model and the schematic network model, sali-ent readings would be those that constitute a semantic center, in the sense thatthey are the basis for numerous semantic extensions. Conceptually, salient read-ings contribute significantly to the semantic coherence of the category; typo-graphically, they are the basis from which multiple extensions to other readingsdepart.

On the other hand, salience may be represented more directly with typo-graphical means, like shading (cf. figure 1) or thicker lines (cf. figure 3). Thisway of representing salience is more generally applicable than the former, pre-cisely because the different indices of salience need not coincide: what is statisti-cally prominent need not be the logical, semantic center of the category. Thisoften happens, for instance, when the center of a category shifts from its etymo-logical origin to one of the extensions arising from that origin. Through semanticreorganisations, the statistically dominant extension would then eventually be-come the new semantic center of things, but at least at one stage of the word'ssemantic history, the most frequent reading need not be the center of semanticcoherence. In this sense, then, a neutral, direct indication of salience will be use-

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ful over and above the indirect indication of salience that derives from the se-

mantic structure of the category.Hierarchical semantic relations receive a less uniform treatment in the three

models. In the radial set model, schematicity may be represented as one particulartype of semantic relation next to many others; graphically, this might take theform of a binary link labeled "schematization" or "generalization" In the sche-matic network model, of course, such links receive a special treatment in thesense that they will invariably be situated along the vertical dimension of thefigure, whereas the other links (like metaphor and metonymy) will be placedalong the horizontal dimension. In the overlapping sets model, the schematizationrelation surfaces in the form of sets encompassing others: any box in the diagramthat properly includes an other box, generalizes over the latter.

One specific case along the hierarchical dimension needs to be mentionedseparately. Individual members of a category are situated at the bottom of a tax-onomy; "individual members" as meant here are primarily conceived of as indi-viduals in a philosophical sense: separate entities rather than groups or classes.Thus, the individual members of bird would be birds (like Pete, your auntie'sparrot) rather than specific classes of birds. In a set-theoretical sense, individualsconstitute singletons. Now, once a representational format contains a mechanismfor depicting hierarchical relations, it can in principle also deal with individualmembers of a category.

However, considering that these individual members belong to the exten-sional level rather than to the intensional level of the category, they may also betreated somewhat differently than the other levels of a taxonomy. Consider theoverlapping sets model. Representing individual members as bundles of features(i.e. overlapping sets) meets with the difficulty that the number of features identi-fying an individual could be unlimited, or at least very large. Rather, individualmembers of a category are often represented by means of "point-like" represen-tations — by listing them with an individual name, so to speak. In the overlappingsets model, this can be achieved by placing individual category members(represented graphically as points, for instance) within the appropriate areasconstituted by the featural sets. In network models, a specific link (like maybe a"membership link") might be used with the same purpose of distinguishing indi-viduals.

Two further nuances are necessary here. First, it would seem that the bottomlevel of a taxonomy may sometimes be shifted somewhat. In figure 1, for in-stance, one could say that "ostrich" and "chicken" etc. are treated as the relevantmembers of the category "bird" (rather than auntie's parrot). This also impliesthat the distinction between the intensional and the extensional level may be sub-

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ject to contextual shifts. In those cases in which they constitute the bottom of thehierarchy, types of birds like "ostrich", "chicken" etc. are treated as the actualmembers of the category "bird", i.e. they are taken to belong to the extensionallevel. If, however, auntie's parrot is added to the set, the extensional level be-comes more specific. Pete the parrot is an extensional token of the intensionaltype "parrot", and of the intensional type "bird"; but in representations like figure1, the category "parrot" is treated as a token of the category "bird", i.e. is treatedas an entity rather than a class.

Second, "individual members" may also be instances of a category as foundin, for instance, corpus-based analyses. If the specific instances of use of thevarious senses of a word are considered members of the extension of the word, areference to illustrative quotations from the corpus can then be incorporated intothe representation in the same way that Pete the parrot would be listed as a mem-ber of the category.

Non-hierarchical semantic relations are treated as binary links in both theradial set and the schematic network model; in the latter, they obviously occuralong the horizontal axis, as the vertical axis is reserved for relations of schema-ticity. Depending on the nature of the link, labels like "metaphor" or "metonymy"or "similarity" (or others) may be attached to the links. In the overlapping setsmodel, on the other hand, a distinction has to be maintained between similarityrelations and relations like metaphor and metonymy. Clearly, similarity relations

Figure 6: The representational scope of theoverlapping sets model

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are represented in the form of overlapping sets defined in terms of the character-istics featuring in the similarity relation. But it is less obvious to represent meta-phor and metonymy in the same way, i.e. on the basis of shared features.

For metaphorical relations, this is not entirely impossible; the "airplane"reading of bird undoubtedly shares the feature of "flying" with (many) birds. Thedifferences between birds and airplanes could then be indicated by adding fea-tures that both readings do not share, such as the fact that the literal reading in-volves living beings while the metaphorical one involves machines. However, ifthe distinction between literal and metaphorical similarity is to be representa-tionally marked, it is advisable to indicate metaphorical relations explicitly bymeans of labelled links.

Such labelled links would seem to be indispensable for representing me-tonymical links at any rate: it is difficult to imagine how metonymical relations ingeneral can be reduced to shared features. The description of metonymy basicallyinvolves relational predicates linking the two readings that are associated throughmetonymy: the extended reading refers to, for instance, something that is part of(or caused by, or contained in, or characterized by, etc.) the referent of the pri-mary reading. This relational nature of metonymy can be most easily representedwith relational means, i.e. by means of labelled links.

In order to further establish the equivalence between the three models, an

Figure 7: The representational scope of theschematic network model

(5) (1) (2) (3) (7) (6)

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abstract example may again be useful. Let us assume we have a lexical itemwhose literal meaning is a cluster of three subsets, constituted by the overlappingfeatures {a} and {b}; also, all instances of the literal reading share feature {c).Three subsets then have to be distinguished: {c,a}, {c,b}, and {c,a,b}. Further,reading {c,b} is metonymically extended towards a reading defined by {d}. Eachof the readings distinguished so far is represented in a corpus by a number ofexamples (in a text corpus, these could be sentences in which the word is used inthe reading in question): examples (1), (2), and (3) exemplify {c,b}; examples(4), (5), and (6) illustrate {c,a,b}, {c,a}, and {d} respectively. There is no exam-ple illustrating {c} in isolation, but there does occur an example (7) exemplifyinga metaphorical extension {e} of {c}. Given the frequency of the examples, {c,b}is clearly more salient than the other subsets. Figures 6-8 (on pages 35-37) illus-trate how the same information may be presented in each of the three representa-tional approaches.

The representation of the discrepancy between intuitive and analyticpolysemy requires further additions to the diagrams exemplified by figures 6-8.In the overlapping sets representation, any area of the entire cluster that is intui-tively felt to be a distinct reading may be singled out by typographical means. Inthe /7/«f-example of figure 1, for instance, the dotted line that indicates that thefeatures 6 and 7, when taken together, do not suffice to define the category in adistinctive fashion, could also be used to indicate that the cluster of sets that fallswithin the range of the dotted line usually functions as a single reading. The net-

Figure 8: The representational scope of the radial set model

metaphor

M) {1){2)(3) (6) (7)

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work representations (i.e. the schematic network and the radial set representation)require the definition of a new type of node, or alternatively, a new type of la-belled link. In fact, in situations like that exemplified by bird, the semantic linkbetween the analytically distinguishable subsets and the intuitive reading couldbe described as one of alleged generalization: the language user so to speak pre-tends that there is a classically definable, unitary concept generalizing over thesemantically more specific applications of the category. Switching from the la-belled links to the nodes, the nodes created by the process of "alleged generaliza-tion" take the form of a disjunction: various definitionally distinct subsets arelumped together as if they constituted a single classically definable concept.

Figure 9 illustrates how a radial set representation may be enriched to incor-porate "alleged generalization" as an example of the way in which intuitive andanalytical conceptions of polysemy need not coincide. Obviously, the radial setrepresentation is decidedly more cumbersome in these cases than the overlappingsets representation: the graphical changes that have to be applied to the figure toachieve the required distinction are more far-reaching than in the other represen-tational format. In principle, however, the representational possibilities are basi-cally the same.

Figure 9: Enriched radial set representation of "bird"

123A5B7or 234567or 23467or 4567or 3567

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5. Concluding Remarks

In various respects, the story told so far is not yet complete. The exploration, thatis, of adequate representational formats for prototype-oriented lexical semanticsshould not stop at the observation that the three formats currently used are no-tional variants (or at least, can be turned into notational variants). Even disre-garding the whole domain of onomasiological research, the following observa-tions have to be made.

First, the representations developed so far do not explicitly provide a placefor syntagmatic data. The readings incorporated into the representations mayeach be subject to specific syntagmatic restrictions. In the case of spatial rela-tional concepts, for instance, a particular relation may occur only with particularpairs of landmarks and trajectors; furthermore, this set of syntagmatic contexts islikely to be subject to typicality effects just like the paradigmatic readings them-selves. The diagrammatic representations, then, will have to be elaborated with afurther layer on which the syntagmatics of each of the paradigmatic readings isspecified.

Second, the notational equivalence of the three models does not imply that nochoices have to be made when working with these formats. There are, for onething, empirical matters to be clarified: what the relevant prototypical centers orthe psychologically real schematic meanings within a concept are, is not some-thing that can be derived from the models as such: it is an empirical matter thathas to be settled before representations are suggested. (In this respect, see Taylor1990 for an insightful discussion of the empirical aspects of choosing betweenprototypicality and schematization; compare also Winters 1992.) For anotherthing, the choice of one form of representation rather than another may be a mat-ter of pragmatic focus: when the research interest lies mainly with definitionalproblems (involving the differences between intuitive and analytical definitions ofpolysemy), the overlapping sets model may be more useful than the radial setmodel. The latter, conversely, may be more appropriate when the focus is onmechanisms of semantic extension, as in diachronic semantics.

Finally, the limits of the representational formats have to be taken into ac-count: the larger the set of relevant semantic dimensions, the more difficult itbecomes to devise a graphical representation that is both elegant and complete.Splitting up the representation in various levels is one way of extending the repre-sentational possibilities: each of the components of a simplified, skeletal repre-sentation at level 1 may then be treated separately and in more detail at level 2.for instance. In general, the representations should not be given absolute value:they merely serve to present a linguistic analysis of word meaning in as clear andsystematic a way as possible. The analysis itself, then, obviously comes first.

40

both logically and chronologically; the representation should never become an

end in itself.

Address of the author:

Dirk GeeraertsDepartement LinguistiekUniversity of LeuvenBlijde-Inkomststraat 21B-3000 Leuven (Belgium)e-mail: dirk.geeraerts@arts.kuleuven.ac.be

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