*Natural Logic and Semantics*

By 'natural logic' here I mean the program of analyzing natural language inference in a way which uses surface sentences as much as possible, and therefore tries to avoid translation into languages such as standard first-order logic. This research area goes back quite far and is experience something of a resurgence due in part to connections to fields like natural language processing.

My talk will have two overall goals: first, to present the area as a whole and to explore implications for, and lessons from, the more standard approach of model-theoretic semantics.

Second, given the MoL audience, I want to present what I think are interesting mathematical results in the area. These have to do with completeness for fragments of language, and in the talk I'll discuss fragments dealing with extended syllogistic fragments involving negation. The completeness for such fragments uses algebraic semantics. This is reminiscent of the use of boolean algebras and their representation theory in propositional contexts. But here we use orthoposets instead, and the work has a somewhat different flavor.

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