A single-type logic for natural language

作者：Liefke Kristina^*

来源：Journal of Logic and Computation, 2015, 25(4): 1111-1131.

DOI：10.1093/logcom/exs074

• Single-type hypothesis
• data semantics
• Montague grammar
• partial logic
• type theory

In this article, we develop a single-type logic for natural language along the lines of [Partee (2009, Snippets, vol. 20)]). This logic, called 'TY03' 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 TY03 and prove its soundness and completeness with respect to the class of models. To show the logic's application adequacy, we provide a TY03 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.

• 出版日期2015-8