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Liefke, Kristina (2013): A Single-type Logic for Natural Language. In: Journal of Logic and Computation
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In this article, we develop a single-type logic for natural language along the lines of Partee (2009, Snippets, vol. 20)). This logic, called `TY30' takes objects of different syntactic categories and model-theoretic domains to be structured by the same logical type. Its language, a variant of the simply typed lambda calculus, is interpreted in partial Henkin models. We give a Gentzen-style sequent calculus for TY30 and prove its soundness and completeness with respect to the class of models. To show the logic's application adequacy, we provide TY30 a semantics for a standard fragment of English. Partial possible worlds, which are identified with elements in the logic's base domain, enable us to obtain the standard modal operators.