Abstract
It has been discussed above that there is not a constructive relevance logic in the RM-semantics if the set of all points does not contain both a subset of designated points and a subset of consistent points. In this chapter, we introduce the logics RBc and RBc2, which are two different versions of the basic constructive relevance logic in RM1-semantics with a set S⊆K (RM-semantics with a set of designated points and a set of consistent points). The logic RBc is built upon the positive language of B+ expanded with the unary connective ¬; the logic RBc2, upon the language of RBc expanded with the propositional truth constant t. A third logic, the logic RB+,t,f, built upon the positive language of B+ expanded with the two propositional constants, t and f, is also introduced. RBc2 and RB+,t,f are definitionally equivalent. We recall that “constructive” is understood as “endowed with an intuitionistic-type negation”; and that L is a relevance logic (in the minimal sense) if it has the “variable-sharing property”.
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