Non-deterministic Semantics for Intuitionistic Paraconsistent Logics

The survey [5] is devoted to paraconsistent extensions of positive classical logics (and especially to C-systems of this kind). It seems however that positive intuitionistic logic is a better starting point for investigating negation. The valid sentences of this fragment are all intuitively correct. Positive classical logic, in contrast, includes counterintuitive tautologies like (A B_C) (A B)_(A C) or ((A B) A) A. Moreover