A small group of linguistic categories forms the backbone of elementary sentence formation, as summed up in the following rewrite rules: S ⇒NPVP NP⇒ PN NP ⇒ Det N; involving the notions of Sentence, Noun Phrase, Verb Prase, Proper Name, Determiner and Common Noun. In what follows, we shall focus on the Noun Phrases in this scheme. Some of their parts seem to be ‘interpretatively free’, in the sense of allowing any available denotation in a model. Thus, in principle, proper names can denote arbitrary individuals, and common nouns can assume arbitrary extension sets of individuals. In contrast, determiner expressions (‘determiners’) form a more structured class, which is reflected in certain constraints on their semantics. Thus, the latter category of expression has been at the centre of attention in recent studies of possible denotations for natural language items. A related, more intrinsic reason is this: determiners provide the ‘conceptual glue’ with which we express basic relations between predicates (denotationally: [Det] ([N], [VP])). Accordingly, determiners will be the first topic in this book, though by no means the last.
KeywordsNoun Phrase Common Noun Categorial Grammar Determiner Relation Actual Infinity
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