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FIRST-ORDER POSSIBILITY MODELS AND FINITARY COMPLETENESS PROOFS

Published online by Cambridge University Press:  02 September 2019

MATTHEW HARRISON-TRAINOR
MATTHEW HARRISON-TRAINOR*
Affiliation:
School of Mathematics and Statistics, Victoria University of Wellington
*
*SCHOOL OF MATHEMATICS AND STATISTICS VICTORIA UNIVERSITY OF WELLINGTON WELLINGTON, NEW ZEALAND E-mail: [email protected]URL: http://homepages.ecs.vuw.ac.nz/~harrism1/
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Abstract

This article builds on Humberstone’s idea of defining models of propositional modal logic where total possible worlds are replaced by partial possibilities. We follow a suggestion of Humberstone by introducing possibility models for quantified modal logic. We show that a simple quantified modal logic is sound and complete for our semantics. Although Holliday showed that for many propositional modal logics, it is possible to give a completeness proof using a canonical model construction where every possibility consists of finitely many formulas, we show that this is impossible to do in the first-order case. However, one can still construct a canonical model where every possibility consists of a computable set of formulas and thus still of finitely much information.

Keywords

03B45modal logicpossibility semanticscompleteness proofs
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 4 , December 2019 , pp. 637 - 662
Copyright
Copyright © Association for Symbolic Logic 2019 

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