Paraconsistent modal logics

Electronic Notes in Theoretical Computer Science 278:173-186 (2011)
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Abstract

We introduce a modal expansion of paraconsistent Nelson logic that is also as a generalization of the Belnapian modal logic recently introduced by Odintsov and Wansing. We prove algebraic completeness theorems for both logics, defining and axiomatizing the corresponding algebraic semantics. We provide a representation for these algebras in terms of twiststructures, generalizing a known result on the representation of the algebraic counterpart of paraconsistent Nelson logic.

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Umberto Rivieccio
Universidad Nacional de Educación a Distancia

Citations of this work

Nelson’s logic ????Thiago Nascimento, Umberto Rivieccio, João Marcos & Matthew Spinks - 2020 - Logic Journal of the IGPL 28 (6):1182-1206.

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References found in this work

Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Foundations of mathematical logic.Haskell Brooks Curry - 1963 - New York: Dover Publications.
How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.

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