An Epistemic Interpretation of Paraconsistent Weak Kleene Logic

Damian E. Szmuc

doi:10.12775/LLP.2019.014

Authors

Damian E. Szmuc Department of Philosophy, University of Buenos Aires and IIF-SADAF, CONICET

DOI:

https://doi.org/10.12775/LLP.2019.014

Keywords

weak Kleene logic, infectious logic, containment logic, sequent calculus

Abstract

This paper extends Fitting’s epistemic interpretation of some Kleene logics to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting’s “cut-down” operator is discussed, leading to the definition of a “track-down” operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, further reflections on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations.

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