Possible-translations semantics for cathodic modal logics

Abstract

This paper discusses the motivations and the possibilities for defining possible-translations semantics (introduced by W. A. Carnielli and further developed by W. A. Carnielli and J. Marcos) to a class of logics that we call cathodic modal logics, defined as extensions of positive modal logics (here called anodic modal logics) by means of consistency (and inconsis- tency) operators. In this way, cathodic modal logics are logics of formal inconsistency (the LFIs, as treated in [CCM07]) enriched with modal op- erators. The material here introduced constitutes first examples of modal systems endowed with possible-translations semantics. The motivations for studying cathodic modal logics stem from the fact that these systems are able to provide alternatives for dealing with some modal paradoxes of diverse kinds, at least the ones engendered by the mixture of the (too strong) classical negation with modal operators.