@article{Szmuc_2019, title={An Epistemic Interpretation of Paraconsistent Weak Kleene Logic}, volume={28}, url={https://apcz.umk.pl/LLP/article/view/LLP.2019.014}, DOI={10.12775/LLP.2019.014}, abstractNote={<p><span lang="EN-US">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.</span></p>}, number={2}, journal={Logic and Logical Philosophy}, author={Szmuc, Damian E.}, year={2019}, month={May}, pages={277–330} }