Adjectives: A Uniform Semantic Approach

Despite their simple syntactic form, adjective-noun combinations seem to have no straightforward semantic method that parallels the simplicity of the syntax. This has led to the conventional belief that adjectives belong to a (semantically motivated) hierarchy. This has the consequence that a uniform treatment of adjectives is unattainable—without resorting to notions such as possible worlds, which are difficult to map into competent computer programs. Moreover, because of their seemingly “undisciplined” semantic behaviour, adjective-noun combinations have been used by some authors (e.g. [5]) to further the argument of non-compositionality of natural-language expressions. Contrary to such views, we believe that adjectives are more systematic in their behaviour than originally thought. In support of this claim and based on typed sets, we propose a uniform approach to the semantics of adjective-noun combinations. It hypothesizes that adjective-noun combinations can semantically be thought of as a set intersection involving the adjective(s) and the head noun of the compound. 1 Adjective Hierarchy: The Conventional View It is a commonly-accepted view that adjectives have different underlying semantic rules (see [1,3,4,6,7,8,9,13,14,16,17]). This has led to the belief that adjectives assume a semantically-motivated hierarchy . This hierarchy is listed below: • Intersective e.g. ‘red’. • Subsective: o Pure, e.g. ‘accomplished’. o Double, e.g. ‘beautiful’. • Non-subsective: o Non-privative or non-committal, e.g. ‘alleged’. o Privative, e.g. ‘fake’. Intersective adjectives are the most restricted ones. The adjective angry in the sentence That man is angry is an example of an intersective adjective. The meaning of angry man then can be computed as the intersection of angry things and men. † Acknowledgement: this work was supported by a discovery grant from the Natural Science and Engineering Council of Canada. 1 A note concerning the terminology is in order. Authors use different terms to describe the different classes of adjectives. In some cases, syntactic and semantic terminologies overlap. Adjectives: A Uniform Semantic Approach 331 The second class of adjectives is called subsective. They are so called because all that can be said about them is that the denotation of an adjective-noun combination is a subset of the denotation of the noun. The adjective ‘accomplished’ is an example of such adjectives. Accomplished in Maria is an accomplished musician does not mean that the denotation of Maria is accomplished and is a musician. All we can say is that Maria is in the set of musicians, i.e. accomplished musicians are musicians. Syntactically, adjectives similar to ‘accomplished’ are always in the attributive position. We term these adjectives “pure subsective” to distinguish them from the other kind of adjective in the same class—the double adjectives. Double adjectives (or doublet as called by [16]) belong to the class of subsective adjectives. Syntactically, these adjectives can be in either position: the attributive or predicative. Semantically, they can have an intersective reading (i.e. referentmodifying) and a subsective reading (i.e. reference-modifying), regardless of their syntactic position. Beautiful in the sentence That dancer is beautiful is an example of a double adjective. Thus, beautiful can either be understood as attributing beauty to the dancing of the denotation of that or the physical beauty to the denotation of that. In the intersective, reading, the denotation of that belongs to the intersection of beautiful things and dancers. In the subsective reading the denotation of that belongs to a subset of the set of dancers, i.e. those who dance beautifully. Finally, there are those adjectives that are neither intersective nor subsective, the so-called non-subsective adjectives. Within this class two sub-classes can be recognized—privative adjectives and non-privative. Adjectives such as ‘former’ and ‘fake’ are privative. They are called privative because the denotation of the privativenoun combination is not a subset of the denotation of the noun, e.g. counterfeit money is not money. The other member of the non-subsective class of adjectives is those adjectives that are non-subsective and non-privative. ‘Potential’ and ‘possible’ are examples of this class. A potential winner may or may not be a winner. In some cases, the classification is not clear-cut. For example, it is debatable, whether the adjective ‘former’ is privative. Also, the so called measure adjectives such as ‘tall’, ‘small’, etc. are considered intersective yet they fail the consistency test. For example, tall in John is a tall surgeon modifies the denotation (that is, the extension) of surgeon rather than meaning (that is, the intension) of surgeon. [3] and [16] argue that measure adjectives are in fact intersective. The failure of the substitutivity (i.e., consistency) test is due to the fact that measure adjectives are vague/context-dependent. The assumption of the existence of the adjectival hierarchy has led to the conclusion that a uniform approach to the semantics of adjectives is possible only if they are treated as functions from properties to properties, i.e. functions from intensions to intensions [4]. This renders a set-theoretic approach to the semantics of adjectives unattainable from the conventional viewpoint. 2 Semantically the most agreed upon classifying criterion is that of intension versus extension or, respectively, reference-modifying versus referent-modifying, as is used in [16]. Siegel uses the consistency test, as many authors do, to tell apart the intensional and extensional adjectives. This test roughly states that when an intersective adjective combines with coextensive nouns, the resulting noun phrases remain co-extensive. 332 N. Abdullah and R.A. Frost 2 Fake Guns Are Guns Language is inherently generative. With its, rather limited, stock of linguistic items it is capable of expressing novel concepts by means of combining existing linguistic items. In some cases, however, and because of the dynamic nature of concepts, new referents may fall under an already-existing concept. For example, in number theory, a number used to denote a natural number. With the conception of negative numbers, the concept “number” encompasses both negative and positive numbers. This process continued (and may continue) to include different kinds of numbers. This is because there is so much in common between the entities or mathematical objects we now call numbers. In everyday language this process, we argue, is generally in use—consider, for instance the category “bird”, as much studied and illustrated in prototype theory and default logics with regard to the property of “flying”—and specifically with regard to privative-noun combinations. A fake gun and a real gun have many properties in common—similarly, an artificial heart and a real heart. In some cases, the distinction between an instance of the denotation of a default-noun combination and that of a privative-noun combination is hard to tell, or requires domain knowledge, e.g. artificial light versus natural light, Table 1—if there is a difference, indeed. If it were for things denoted by a privative-noun combination not to fall under the extension denoted by the noun, there might have been a dedicated lexeme—interestingly, even the word robot (i.e. a single linguistic item) is originally chosen by the Czech playwright Karl Čopek (1890-1938) as a more suitable term for “artificial workers” in his play Rossum's Universal Robots . Of course, this is not to claim that a concept must be denoted by a single lexeme. What is meant, however, is that the frequent use of a concept is usually reflected in language by being represented by a single linguistic symbol, as is the case with common nouns. Therefore, in answering the question of what is a fake gun, we argue that it is a gun, provided that fake and real guns are subsumed by the term ‘gun’. The notion of augmenting the concept, or equally the extension, denoted by the noun in an adjective-noun combination, is linguistically supported. In language, it is noticed that all privative adjectives have antonyms/contrasts, e.g. intensifiers. Privatives such as fake, artificial, and false have antonyms/contrast, respectively, real/genuine, natural, and true. It seems that there is a strong pairing between privatives and their (intensifier) counterparts to the extent that the use of the privative antonym is meaningless, if possible indeed, in isolation with its counterpart. The intensifier is usually implicit. Most of the time it is considered default or redundant when there is no ambiguity. The compound real fur is deemed necessary only when there is fake fur in the vicinity. [12] reaches the conclusion that privative adjectives are subsective based on work done by other researchers (e.g., see, [11]) on the “Noun Phrase-split phenomena” in Polish, which reveals the absence of the privative adjective class in Polish. That is, the presence of the privative class of adjectives is an idiosyncrasy of some languages and English is one of them. 3 See, http://capek.misto.cz/english/interesting.html for a translation of an article by the author of the play in the Lidove Noviny, 24.12.1933. Adjectives: A Uniform Semantic Approach 333 Table 1. Missing properties Adjective Phrase Property missing from the default set of features Artificial heart e.g. not flesh-and-blood Artificial flower e.g. doesn’t grow Artificial light e.g. source Former senator e.g. temporal continuance False teeth e.g. not naturally grown Cloned sheep e.g. not naturally bred Virtual reality e.g. exists visually only Imitation leather e.g. genuineness Wooden lion e.g. “make-ness”—physical and non-living Fake statue e.g. originality Fake perfume e.g. substance/originality In short, intensifier/privative seem to be (semantically) intimately related. If viewed as functions, they can be thought of as functions and their respective inverse functions. Alternatively, they can be viewed as set partitions of the set N, which represents the denotation of the noun an intensifier/privative pair combines with. The latter view is adopted in the approach proposed in this paper. In our view, both “regular” adjectives such as ‘red’, ‘angry’, or ‘skillful’ and privative adjectives such as ‘fake’ or ‘former’ have one thing in common. They both pick out or further constrain the domain denoted by the noun of the compound. They differ in the means of doing it: regular adjectives by highlighting some property or properties of the noun, while privative adjectives by “masking” some property or properties of the noun. Once the argument of augmenting the denotation of common nouns is accepted, expressions such as that senator, that gun, and that heart are considered elliptic forms, respectively, for that current senator, that real gun, and that natural heart. However, privative-common-noun combinations should be explicitly specified, i.e. that former senator, that fake gun, and that artificial heart. The view that privative adjectives are subsective, results in the following adjective hierarchy: • Intersective. • Subsective: o Pure. o Double. o Privative. This analysis makes it possible that a generalized set-theoretic approach to adjectives is attainable. 4 In some settings the opposite is true. For example, in a tòy store (i.e., a store that sells toys) the term gun would more plausibly mean a fake gun. Thus, fake gun is the default. 334 N. Abdullah and R.A. Frost