Studies on advanced paraconsistent modal logic

Abstract

This project aims to a study of two wide families of non-classical logics: modal logic and paraconsistent logic. The study will not bedone through a comparative analysis, but by the production of new systems, operators and branchs of modal logic. This project investigates an advanced study of paraconsistent modal logic, forinstance of modal LFIs, an ample and expressive class of paraconsistent logic that internalizes the consistency and inconsistency notions in the object-language.Such advanced study encompasses notions such as generalized frames, algebra, bissimulation, model theory, and so on. The paraconsistent version of such notions is obtained by using, on the one hand, non classical algebrizations of Blok-Pigozzi and, on the other hand, taking into account the recent results of completeness for first order LFIs.Another goal towards an advanced study of modal logic is the analysis of modal incompleteness results and the definition of extensions ofmodal logic. Concerning the latter, this project focuses on the so called hybrid logics, an Extension of modal logic which shows to be a wide and fruitful field of research. (AU)