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