An Ontological Semantic Account of Relative Quantification in English

This paper proposes a linguistic analysis of the semantic behavior of relative quantifiers in English, those for which an absolute value cannot be determined, with attention to the differences in properties and meaning between individual quantifiers and the semantic subclasses created by these quantifiers. Represented formally within Ontological Semantic Technology (OST), the semantic nature of such relative quantifiers is also described for computational purposes, with consideration of the related mathematical qualities of quantification that must be captured for adequate description. Among the English quantifiers considered here are few, a few, little, a little, a bit, some, several, many, much, most, a lot, the comparative forms of more, less, and fewer, compositions of combined relative quantifiers, such as much more, and the intensification of quantification with very and too. Quantification in English can occur in two forms, as absolute with numerical equivalents or as relative with variable, inconsistent values that appear to be contextually dependent. Relative quantification, the focus of this paper, has been commonly treated with syntactic analyses, with quantifiers seeing little in the way of meaningful semantic descriptions. A large portion of these syntactic accounts aim at describing quantification through solely formal mathematical and logical representations (Keenan 1973; Partee 1978; Barwise and Cooper 1981; Keenan and Stavi, 1986), despite both realms failing to produce any definable subclasses or conclusive semantic properties for further application due to their inabilities to represent the syntactic relationships of natural language and the minor distinctions of quantifier meaning (Nirenburg and Raskin 2004). However, existing linguistic descriptions of quantifier behavior has provided some insight into their semantics. Jespersen’s earlier work (1933) is absent of the term quantifier, discussing instead only indefinite numerals and totality, the latter in keeping with Sapir’s (1930) discussion of the meanings of all, with some consideration of each and every. While Jespersen’s (1969) later description contributes adjectival modification (few women, three students), he shows the beginning of a semantic characterization with the note that quantifiers vary from syntactically similar adjectives in that they do not mark anything about kinds, only numbers. Quirk et al. (1985) set up a more detailed syntactic description regarding quantifiers’ nominal co-occurrence but provide little toward semantic descriptions. Keenan and Stavi (1986) touch on the semantics of quantifiers in their description of natural language determiners of some, several, few and most, but view them in light of determiner behavior for a limited analysis which gives more attention to the behavior of the syntactic class rather than the semantic phenomenon of quantification. In their work on the psychology of quantifiers, Sanford, Moxey, and Paterson (1994) consider two classes of relative quantification—though, oversimplifying the task greatly—as denoting only small or large amounts, leaving middle-range quantifiers in their overlapping boundaries and awkwardly classified as a result. However, there lies in English quantification more than simple proportional comparisons and syntactic descriptions. The simplest case of English quantification is that provided by numerals, which give exact amounts, and their lexical and morphological equivalents, such as singular nouns. However, some English quantifiers offer a relative quantification for which a numerical equivalent cannot be consistently established (Bradburn and Miles 1979; Routh 1994; Wright et al. 1994). Consequently, some researchers argue that the conceptual definition of a linguistic quantifier should be no more than a variable reference point (Sanford, Moxey, and Paterson 1994), eliminating the general notion of a lexical class (Nouwen 2010). Contrary to this belief, the behavior of relative quantifiers can be shown to create a cohesive netting of lexical items with similar semantic meaning. When 1 For a similarly computational account of numerals, see Taylor et al.