Abstract

A system is classified as multimodal if its language has more than one modal operator as primitive, and such operators are not interdefinable. We extend the anodic and cathodic modal systems, introduced in Bueno-Soler and Bueno-Soler , to a class of the so-called basilar multimodal systems generating, in this way, the classes of anodic and cathodic multimodal logics. The cathodic multimodal systems are defined as extensions of positive multimodal systems by adding degrees of negation plus consistency operators. In this way, cathodic multimodal systems are logics of formal inconsistency [the paraconsistent LFIs, as treated in Carnielli et al. ] enriched with multimodal operators. We focus the attention on models for such classes of systems and discuss how modal possible-translation semantics, as well as possible-worlds , can be defined to interpret basilar cathodic multimodal systems. While anodic systems are modeled by Kripke models only, we introduce the modal possible-translation models for cathodic systems. Such models, given by combinations of three-valued modal logics, besides their own interest, explain the role of non-trivializing contradictions in multimodal environment