klecha (2012)
Klecha, Peter. 2012. Positive and conditional semantics for gradable modals. To appear in Proceedings of Sinn & Bedeutung 16. The pdf below is a pre-publication draft. It differs from the version to be published only in style and a few minor corrections.

Keywords. modality, gradability, scale structure, conditionals

Abstract. This paper presents a semantics for gradable modal adjectives (GMAs), focusing particularly on likely. Lassiter (2010, 2011) argues that the adjectives possible, likely, and certain have a common, gradable, probability-based semantics, on the basis of entailment relations between these terms. This claim contradicts Kennedy's (2007) Interpretive Economy which predicts that adjectives with the same scales should have the same positive interpretations. I argue that these adjectives do not provide a counterexample to Interpretive Economy, and give a semantics for them which preserves the entailment relations discussed by Lassiter, while also preserving the general theory of modality (Kratzer 1981, 1986); to this end I show that one important aspect of Kratzer's analysis, the analysis of conditionals as domain restrictors (Kratzer 1986) can be preserved for gradable modals.