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 |
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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 |
Item ID: | 21046 |
Date Deposited: | 03. Jul 2014, 06:44 |
Last Modified: | 04. Nov 2020, 13:01 |