LITTLE: Not a Dichotomy-Based Negation Operator, but a Trivalence-Based Polar Opposition Operator
Linmin Zhang and Jia Ling
590-598 (complete paper
or proceedings contents
This paper focuses on the semantics of natural language polar opposition in using scalar adjectives. Based on the interpretation of (i) neither many nor few and (ii) less tall than, this paper argues against the traditional view that polar opposition is equivalent to dichotomy-based set-theoretic negation (i.e., a distinction between a set and its complement). Instead, this paper proposes that polar opposition should be analyzed as a scale-based trivalent distinction, i.e., a distinction among a positive value on a scale, its negative inverse, and the neutral value between them. This paper also emphasizes that this neutral value on a scale is not an 'extension gap,' but rather the intersection of two 'negative extensions.' The formalism of the analysis is implemented with interval arithmetic. Moreover, by analyzing the direction of inequality in comparatives as the polarity of differentials, the paper further provides a unified account for the use of little and few in both absolute constructions and comparatives.
Proceedings of the 34th West Coast Conference on Formal Linguistics
edited by Aaron Kaplan, Abby Kaplan, Miranda K. McCarvel, and Edward J. Rubin
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