Word Classes in Formal Semantics

Formal semantics of natural language grew out of works that assume a strong relationship between syntactic categories and semantic types (Lewis, 1970; Montague, 1973). In its strictest formulation, this assumption entails that any two words of the same category must have the same type of meaning. Thus, by learning the morpho-syntactic category of a word, you learn some of its most important semantic aspects. This idea is theoretically appealing but it comes with a heavy toll. A too restrictive matching between syntactic categories and semantic types is descriptively untenable. In many languages, one and the same word class may systematically correspond to more than one semantic type, or contribute to sentence meaning in ways that are not easy to describe using types alone. Much of the progress in formal semantics since the 1970s has been achieved by articulating a richer palette of semantic objects suitable for describing meanings of the major word classes in Germanic and Romance languages. This has been accompanied by a principled relaxation of the matching between categories and types. Starting from the mid-1990s, much research in formal semantics has been devoted to less well-studied languages (Von Fintel and Matthewson, 2008), with a more recent keen interest in the cross-linguistic analysis of categories in formal semantics (Francez and Koontz-Garboden, 2017). One of the assets of formal semantics is its explicitness regarding processes of nominal quantification and anaphora. This has led to a focus on the semantics of nouns and its extensions to other categories. The semantic connections between nouns and other word classes are also the main topic of this paper. To review this state of the art, section 1 starts out by introducing the classical notion of types in formal semantics, which describe functionargument relations like those that appear between verbs and their arguments, or between determiners and nouns. We illustrate this ‘extrinsic’ use of types in analyses of English and of Warlpiri, whose word order is freer and case system is richer than most European languages. Extrinsic typing does not distinguish nouns from verbs, adjectives and prepositions. These word classes are distinguished by their phrase-internal semantic arguments, which play a central role in modification. This is the topic of section 2. The analysis of phrasal modifiers allows us to characterize category-specific arguments for meanings of verbs (states and events), gradable adjectives (degrees) and locative prepositions (spatial objects). Unlike these other word classes, nouns are assumed not to have intrinsic semantic arguments, and their extrinsic entity argument is directly targeted by phrase-internal modifiers. Section 3 addresses another property that distinguishes nouns from other categories: their ability to restrict the domain of quantification. This property of N-conservative quantification, together with phrase-internal modification, are illustrated by analyzing the semantic disambiguation of N/V-like words in Hebrew. Section 4 addresses another characteristic of nouns: their ability to introduce identity criteria, as proposed in the philosophical work of Geach (1962).