Abstrakt
We investigate logics which expand the four-valued Belnap-Dunn logic by a notion of inconsistency. In order of increasing expressive power, this can take the form of an expansion by an inconsistency predicate, an inconsistency constant, or a reductio ad contradictionem negation.
After briefly motivating the study of inconsistency and reviewing some related work, we introduce these logics as the quasiequational logics of a certain class of algebras and then discuss their relational semantics. This leads us to a logic which is a natural conservative extension of both classical and intuitionistic logic.