Interpretations of Negative Degree Sentences and Questions

The interpretations of degree expressions require the postulation of new entities to represent degrees. Diverse entities such as degrees, intervals, and vectors are adopted for degree expressions. Positive degree sentences and questions are properly construed with the introduction of these entities, but their negative counterparts need more consideration. Negative degree sentences show dual patterns of entailments depending on contexts, and negative degree questions are unacceptable, making weak islands. To explicate the distinct nature of negative degree sentences and questions, Fox & Hackl (2006) provide an analysis based on degrees while Abrusan & Spector (2010) suggest a proposal in interval readings of degree expressions. I have pointed out the theoretical problems of these analyses and proposed an alternative in the framework of the vector space semantics, following Winter (2005). Bi-directional scales in vector space fit well with the dual patterns of negative degree sentences, and the notion of a reference vector is useful to accommodate the contextual influence in negative degree sentences and to deal with the unacceptability of negative degree questions.