Semantics for a basic relevant logic with intensional conjunction and disjunction (and some of its extensions)

摘要

This paper proposes a new relevant logic B_(∩∪)~+, which is obtained by adding two binary connectives, intensional conjunction n and intensional disjunction ∪, to Meyer-Routley minimal positive relevant logic B~+, where n and U are weaker than fusion o and fission +, respectively. We give Kripke-style semantics for B_(∩∪)~+, with →, ∩ and ∪ modelled by ternary relations. We prove the soundness and completeness of the proposed semantics. A number of axiomatic extensions of B_(∩∪)~+, including negation-extensions, are also considered, together with the corresponding semantic conditions required for soundness and completeness to be maintained.