An Algebraic View of Super-Belnap Logics

Studia Logica 105 (6):1051-1086 (2017)
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Abstract

The Belnap–Dunn logic is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point of view ofAlgebraic Logic, exploring applications of the general theory of algebraization of logics to the super-Belnap family. In this respect we establish a number of new results, including a description of the algebraic counterparts, Leibniz filters, and strong versions of super-Belnap logics, as well as the classification of these logics within the Leibniz and Frege hierarchies.

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Author's Profile

Umberto Rivieccio
Universidad Nacional de Educación a Distancia

References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
On notation for ordinal numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.

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