Alternative comparison in underspecified degree operators

This paper proposes a new theory for the recurrent ambiguities between the meaning of comparison, additivity, and continuation (CAC) across languages. The theory has two pillars. One is a semantic reanalysis of CAC meanings. I will show that all three meanings can be cashed out via comparisons between alternatives, and that by doing so we can establish inherent logical connections between them. The second pillar is a de-compositional analysis of lexical items expressing CAC meanings (henceforth CAC operators), which makes use of their logical connections to derive the ambiguities as results of underspecification.