PARANORMAL MODAL LOGIC - PART II: K-?, K AND CLASSICAL LOGIC AND OTHER PARANORMAL MODAL SYSTEMS

In this two-part 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.