An Epistemic Interpretation of Paraconsistent Weak Kleene Logic

SZMUC, DAMIÁN ENRIQUE

LOGIC AND LOGICAL PHILOSOPHY

Nicolaus Copernicus University

Lugar: Toruń; Año: 2019 vol. 28 p. 277 - 330

1425-3305

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.