Juliana Bueno-Soler (Centre of Natural Science and Humanities (CCNH), Brazil) intervient sur "Modal systems with nuances in negation: from completeness to incompleteness".
We call anodic the purely positive versions of modal systems, and cathodic any non-classical (w.r.t. negations) version of modal systems. Paradigmatic examples of the latter are modal paraconsistent systems based upon logics of formal inconsistency (LFIs), i.e., based upon paraconsistent systems where the concept of consistency is internalized within the object language, so as to control the “strength” of negation inside the systems. We discuss here some strategies for obtaining completeness to cathodic systems,as well as some limitative results concerning incompleteness, emphasizing the role of negation in such constructions.