Semantics for a Basic Relevant Logic with Intensional Conjunction and Disjunction

This paper proposes a basic relevant logic with intensional conjunction ⊓ and disjunction ⊔, which are more primitive than those defined by A∘B=df¬(A→¬B) and A+B=df¬A→B. is a conservative extension of the basic relevant logic B+. Stronger logics can be obtained by adding axioms or rules to . Kripke style semantics for is given. Three ternary relations R, S1, S2 are used to deal with →, ⊓, and ⊔, respectively. We also consider negation-extensions of . The '*' operator is used to model negation.