Natural Logic and Semantics

Two of the main motivations for logic and (model-theoretic) semantics overlap in the sense that both subjects are concerned with representing features of natural language meaning and inference. At the same time, the two subjects have other motivations and so are largely separate enterprises. This paper returns to the topic of language and logic, presenting to semanticists natural logic, the study of logics for reasoning with sentences close to their surface form. My goal is to show that the subject already has some results that natural language semanticists might find interesting. At the same time it leads to problems and perspectives that I hope will interest the community. One leading idea is that the target logics for translations should have a decidable validity problem, ruling out first-order logic. I also will present a fairly new result based on the transitivity of comparative adjective phrases that suggests that in addition to 'meaning postulates' in semantics, we will also need to posit 'proof principles'.

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