The concept of strong F-paraconsistency

Abstract

We shall consider propositional languages with a propositional falsity constant F. Following Priest and Tanaka (cf. [1]), a logic S could be defined as F-paraconsistent iff F² A is not a rule of S. This conept  of paraconsistency is, however, too permissive because, according to it, minimal intuitionistic logic J m, e.g. , is then, a F-paraconsistent logic.But F-inconsistent J m theories are quasi-trivial. The aim of this paper is to define the concept of strong F-paraconsistency (F-Sparaconsistency)and to define the basic constructive F-Sparaconsistent logics, as well as  their extensions in the ternary relational semantics.