Agnostic possible worlds semantics

Authors:
Andrew Plummer;Carl Pollard
Affiliations:
The Ohio State University, Columbus, OH;The Ohio State University, Columbus, OH
Venue:
LACL'12 Proceedings of the 7th international conference on Logical Aspects of Computational Linguistics
Year:
2012

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Introduction to higher order categorical logic

Introduction to higher order categorical logic
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Journal of Logic and Computation
Are (linguists') propositions (topos) propositions?

LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics

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Abstract

Working within standard classical higher-order logic, we propose a possible worlds semantics (PWS) which combines the simplicity of the familiar Montague semantics (MS), in which propositions are sets of worlds, with the fine-grainedness of the older but less well-known tractarian semantics (TS) of Wittgenstein and C.I. Lewis, wherein worlds are maximal consistent sets of propositions. The proposed agnostic PWS makes neither montagovian nor tractarian ontological commitments, but is consistent with (and easily extensible to) either alternative (among many others). It is technically straightforward and, we believe, capable of everything linguists need PWS to do, such as interfacing with a logical grammar and serving as a basis for dynamic semantics.