A Single-type Logic for Natural Language

Liefke, Kristina (2013): A Single-type Logic for Natural Language. In: Journal of Logic and Computation

Abstract

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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic; Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Metaphysics and Philosophy of Language
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 100 Philosophy and Psychology > 160 Logic
• ISSN: 1465-363X
• Language: English