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NEIGHBOURHOOD CANONICITY FOR EK, ECK, AND RELATIVES: A CONSTRUCTIVE PROOF

Published online by Cambridge University Press:  02 July 2021

FREDERIK VAN DE PUTTE  and
PAUL MCNAMARA
FREDERIK VAN DE PUTTE
Affiliation:
ERASMUS INSTITUTE FOR PHILOSOPHY AND ECONOMICS ERASMUS UNIVERSITY OF ROTTERDAM AND CENTRE FOR LOGIC AND PHILOSOPHY OF SCIENCE GHENT UNIVERSITY, GHENT, BELGIUME-mail: Vandeputte@esphil.eur.nl
PAUL MCNAMARA
Affiliation:
PHILOSOPHY DEPARTMENT UNIVERSITY OF NEW HAMPSHIREDURHAM, NH, USAE-mail: Paul.McNamara@unh.edu
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Abstract

We prove neighbourhood canonicity and strong completeness for the logics $\mathbf {EK}$ and $\mathbf {ECK}$ , obtained by adding axiom (K), resp. adding both (K) and (C), to the minimal modal logic $\textbf {E}$ . In contrast to an earlier proof in [10], ours is constructive. More precisely, we construct minimal characteristic models for both logics and do not rely on compactness of first order logic. The proof involves a specific circumscription technique and quite some set-theoretic maneuvers to establish that the models satisfy the appropriate frame conditions. After giving both proofs, we briefly spell out how they generalize to four stronger logics and to the extensions of the resulting six logics with a global modality.

Keywords

classical modal logicaxiom Kneighbourhood semanticscanonical completenessChellas
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 3 , September 2022 , pp. 607 - 623
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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