FIRST-ORDER POSSIBILITY MODELS AND FINITARY COMPLETENESS PROOFS

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 logi...

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Bibliographic Details
Published in:The review of symbolic logic 2019-12, Vol.12 (4), p.637-662
Main Author: HARRISON-TRAINOR, MATTHEW
Format: Article
Language:English
Subjects:
Completeness
Construction
Logic
Semantics
Variables
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Summary: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.
ISSN:1755-0203
1755-0211
DOI:10.1017/S1755020319000418