Comparison and superlatives : what's the best?

Abstract: "This paper investigates several phenomena of superlatives, contrasts them with documented observations about the comparative, and proposes a theory for the semantics of the superlative. Superlatives will be explored with respect to such properties as ambiguity, operator scope, polarity environments, negation, interactions with modality, and inferential behavior. A brief survey of degree variable, extent variable, difference variable, and interpretive approaches will explore the possible paradigms for a theory of superlatives. The necessity for a new theory, treating the superlative as an independent phenomenon related in part to the comparative, will be demonstrated. The resulting proposal is based on a Klein-style model-theoretic extent-based account for comparatives, augmented with a Larson-style lambda calculus approach for operator-based representation of scopal phenomena. Attempts to directly apply comparative theories to the superlative are shown to be inadequate, though initial formulations from the comparative are adopted. These are refined with the addition of two semantic constraints, the exclusion constraint and the membership constraint. The membership constraint imposes a set inclusion constraint on the head of the superative [sic]; the exclusion constraint enforces set complementarity upon the second comparand. The final result is a higher-order logic account for the meaning of the superlative which supports several of the superlative- related observations introduced. Its compatibility with several standard assumptions from the comparative theories, including implicitude and uniqueness, are demonstrated. Finally, future directions are indicated along which the foundation laid in this paper could be pursued."