Many-Valued Modalities and Paraconsistency

This paper extends the three-valued paraconsistent logic LFI1 to a class of multimodal systems, generating an infinite hierarchy of three-valued paraconsistent multimodal logics. LFI1, a member of the family of Logics of Formal Inconsistency, is now enriched with multimodal operators. A system is classified as multimodal if its language has more than one modal operator as primitive and such operators are not interdefinable. We provide possible-worlds (or Kripke semantics) characterizations for all such multimodal logics by means of natural canonical models ruled by a relation algebra, and discuss some aspects connected to the interpretation and uses of such logics.