Paranormal modal logic – Part I. The system K? and the foundations of the logic of skeptical and credulous plausibility

Ricardo Sousa Silvestre

doi:10.12775/LLP.2012.005

Authors

Ricardo Sousa Silvestre Federal University of Campina Grande

DOI:

https://doi.org/10.12775/LLP.2012.005

Keywords

paraconsistent logic, paracomplete logic, modal logic, inductive plausibility

Abstract

In this two-parts paper we present paranormal modal logic: a modal logic which is both paraconsistent and paracomplete. Besides using a general framework in which a wide range of logics  including normal modal logics, paranormal modal logics and classical logic can be defined and proving some key theorems about paranormal modal logic (including that it is inferentially equivalent to classical normal modal logic), we also provide a philosophical justification for the view that paranormal modal logic is a formalization of the notions of skeptical and credulous plausibility.

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