Modal Extensions of Sub-classical Logics for Recovering Classical Logic

Logica Universalis 7 (1):71-86 (2013)
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Abstract

In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to recover the theorems of propositional classical logic within three sub-classical modal systems

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Marcelo Coniglio
University of Campinas

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References found in this work

An introduction to modal logic.G. E. Hughes - 1968 - London,: Methuen. Edited by M. J. Cresswell.
An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Algebraic semantics for modal logics I.E. J. Lemmon - 1966 - Journal of Symbolic Logic 31 (1):46-65.

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