Possible-translations semantics for some weak classically-based paraconsistent logics

This note provides interpretation through possible-translations semantics for a couple of fundamental paraconsistent logics extending the positive fragment of classical propositional logic. The logics PI, Cmin, CLuN, bC, Ci, among others, are all initially presented through their bivaluation semantics and sequent versions and then split by way of possible-translations semantics —the set of 3-valued matrices of the ingredient logics is put forward, together with the set of admissible translating mappings, in each case. Precise statements and all non-obvious details of proofs are supplied. Other details are left to the reader.