An Epistemic Interpretation of Paraconsistent Weak Kleene Logic

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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, rendering 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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Archival date: 2018-08-16
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On Paraconsistent Weak Kleene Logic: Axiomatisation and Algebraic Analysis.Bonzio, Stefano; Gil-Férez, José; Paoli, Francesco & Peruzzi, Luisa
Relevant Logics and Their Rivals.Routley, Richard; Plumwood, Val; Meyer, Robert K. & Brady, Ross T.

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