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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) ; Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) > Logic ; Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) > Metaphysics and Philosophy of Language
• Themengebiete: 100 Philosophie und Psychologie > 100 Philosophie ; 100 Philosophie und Psychologie > 160 Logik
• ISSN: 1465-363X
• Sprache: Englisch