An epistemic interpretation of paraconsistent weak Kleene logic

• Autores: Szmuc, Damián Enrique
• Año de publicación: 2019
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: CONTAINMENT LOGIC; INFECTIOUS LOGIC; SEQUENT CALCULUS; WEAK KLEENE LOGIC
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Szmuc, Damián Enrique. Universidad de Buenos Aires. Facultad de Filosofía y Letras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; Argentina