The operation of negation on combinations of natural categories was examined in two experiments. In the first, category membership ratings of lists of items were obtained for pairs of concepts considered individually, and in two logical combinations: conjunctions (for example, Tools which are also Weapons) and "negated conjunctions" -forms of those conjunctions in which the modifier noun category was negated (Tools which are not Weapons). For conjunctions, results supported earlier findings of overextension, and the geometric averaging of constituent membership values (Hampton, 1988b). Previous findings of concept dominance and non-commutativity within conjunctions were also replicated, both for typicality ratings and for probability of class membership. For negated conjunctions, the pattern of dominance was similar, but interacted with order within the conjunction. Negated conjunctions were also overextended. The second experiment explored how the attributes of negated conjunctions are derived from those of the two component concepts. Frequency of generation of attributes expressed positively (has wheels) or negatively (has no wheels) followed rated frequency in the negated category. The distinctiveness of an attribute to distinguish the complement from the head noun class was associated with the generation of attributes, particularly when there was relatively high overlap between the two categories. Conceptual combination and negation 3 Conceptual Combination: Conjunction and Negation of Natural Concepts The study of conceptual combination has recently come to assume considerable theoretical importance for psychological theories of concepts (Hampton, 1996a; Rips, 1995). The prototype theory of concepts (Rosch, 1978; Rosch & Mervis, 1975) postulated that the classification of objects in categories such as Furniture or Sports is based on the overall similarity structure of the items composing the category. The theory proposed that the category is represented by a prototype, which is an idealized representation of the set of attributes positively associated with category membership. Items are judged to belong in the category if they are sufficiently similar to the prototype (and dissimilar from the prototypes of contrasting categories). Against the prototype theory, it has been argued (Fodor, 1994; Osherson & Smith, 1981, 1982) that the lack of any clear set of rules for combining prototype concepts in logical combinations casts grave doubt on the general value of prototype theory as a theory of human concepts. Hence research on how logical functions operate on prototype concept categories is of considerable theoretical interest. The arguments surrounding this issue have been widely aired (Cohen & Murphy, 1984; Hampton, 1987, 1988b, 1991, 1996a, 1996b; Jones, 1982; Murphy, 1988; Murphy & Spalding, 1995; Osherson & Smith, 1981, 1982; Rips, 1995; Smith & Osherson, 1984; Thagard, 1983; Zadeh, 1982). 1 The problem addressed in this article is how similarity-based prototype concepts enter into logically constructed complex concepts. In particular the focus here is on the logical operations of conjunction and negation. In order to study these operations, the studies to be reported used a head noun plus relative clause construction as a means of expressing conjunction ("Tools which are weapons"), and a similar construction with a negated modifier noun ("Tools which are not weapons") as a means of studying the effect of negation. The questions raised were first, to what extent is category membership in such classes predictable from category membership in each of the constituent classes, and second, to what extent are the attributes which are considered descriptive of the negated conjunctions also true of the constituent classes. Conceptual combination and negation 4 Much current theorizing on the formation of conjunctive concepts has arrived at the view that the most fruitful theoretical approach is an intensional one (Cohen and Murphy, 1984; Hampton, 1987; Smith & Osherson, 1984; Smith, Osherson, Rips, & Keane, 1988). This is to say that rather than modelling membership in the conjunction extensionally in terms of some function of degree of membership in the constituent classes (see for example the fuzzy logic approach, Zadeh, 1965, 1982, or the statistical approach proposed by Huttenlocher & Hedges, 1994), models of conceptual conjunction should aim to define how the two prototypes (or schemas) representing the two concepts become combined into a modified or composite representation of the conjunctive class. (Dissenting accounts are offered by Chater, Lyon & Myers, 1990, and Huttenlocher & Hedges, 1994.) Two intensional models have been developed for concept conjunctions with some degree of detail. Smith et al. (1988) proposed a selective modification model for adjectivenoun combinations such as "Red Apple". In their model a head noun such as "Apple" is represented by a frame (Minsky, 1975) composed of attributes such as COLOR, SIZE or TASTE, each of which can take values, such as red, large, or sweet respectively. Specifically, the representation of the head noun "Apple" would possess an attribute for COLOR which would normally take a range of values -red, green, yellow et cetera -each with an associated number of votes, reflecting its frequency of occurrence as the color of an apple. According to the model, this head noun frame becomes selectively modified in the combination "Red Apple", by switching all the votes for COLOR to the value red, while at the same time increasing the overall weight of color in the determination of similarity to the concept schema. The second intensional model was proposed by Hampton (1987, 1988b) in order to account for the way people understand the conjunction of two noun concepts in phrases such as "Sports that are also games", or "Tools that are also weapons". Hampton's composite prototype model for conjunctions proposed that each noun concept is represented by a prototype, consisting of a list of attributes or properties. When the concepts are conjoined, Conceptual combination and negation 5 then a new composite prototype is constructed by merging together the two sets of attributes defining the two constituent noun concept prototypes. This composite list of attributes is then subject to further modification in order to satisfy various constraints, such as Necessity (an attribute that is considered necessary for a constituent is also considered necessary for the conjunction), Impossibility (an attribute that is considered impossible for a constituent is also considered impossible for the conjunction), and Coherence (the composite prototype may not contain two incompatible attributes). A similar formal approach has been suggested by Thagard (1983, 1995). Apart from being directed at different forms of conjunction, an important difference between the Smith et al. and Hampton models lies in their assumptions concerning the determination of set membership in the conjunctive class. Whereas Hampton (1987, 1988b) explicitly proposed that membership in the conjunction is determined by similarity of instances to the composite prototype, Smith et al. (1988) chose to limit their model to the determination of typicality or representativeness of instances in the conjunction. They recognised that, as constituted, their model failed to pick out a conjunctive concept category which would actually be the logical intersection of the two constituent sets (the same is true of Hampton's model). Quite simply, a logical intersection requires that membership in the conjunction should depend on the level of similarity to each constituent independently. Degree of Redness and degree of Appleness for example should form independent criteria, both of which need to be achieved for something to count as a Red Apple. However if membership of the conjunction Red Apple is based on overall similarity to the conjunctively modified schema, then this independence of criteria will not be possible (see Ashby & Gott, 1988, for discussion of this issue.). For Hampton (1988b), this failure of intensional models to generate intersective conjunctions was taken as a virtue, in as much as his data apparently showed that people's classification of instances in conjunctions was not in fact purely intersective, but showed the kind of interdependence predicted by the models. Smith et al. (1988) in contrast, argued that Conceptual combination and negation 6 typicality and membership depend on two different types of semantic information. They suggested that concepts may have a core meaning some central definitional component of the attribute structure associated with the concept which is used in making class membership judgments, (see also Miller & Johnson-Laird, 1976). If this core is defined as a necessary and sufficient set of common elements, then Boolean set logic can be used to determine how concepts combine. Effectively an object is actually classified as a red apple, only if it has the "core" features of both redness and appleness (no pun intended). Typicality judgments however would be based on similarity using the full range of prototype attributes, and so would not follow logical intersection. Their model for concept conjunction was therefore explicitly restricted in its scope to intuitions of typicality. The primary aim of the present research is to replicate and to extend the range of data considered by such models by exploring the use of negation in conceptual combinations. There has been very little research on how people interpret negated concepts. One obvious reason is that single negated terms have little meaning. People cannot sensibly rate items for their typicality as "not sports". The category is infinite and indefinitely heterogeneous. Within a conjunctive phrase however the task is quite meaningful. Thus "Games which are not sports" is a concept for which participants can sensibly judge the membership and typi
City Research Online Conceptual Combination and Negation 1 Conceptual Combination: Conjunction and Negation of Natural Concepts Conceptual Combination and Negation 2
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