Self-Extensionality of Finitely-Valued Logics

We start from proving a general characterizationof the self-extensionality of sentential logicsimplying the decidability of this problemas for (possibly, multiple) finitely-valued logics.And what is more, in case of finitely-valued logicswith equality determinant as well as either implicationor both conjunction and disjunction, we then derive a characterization yielding a quite effective algebraic criterion ofchecking their self-extensionalityvia analyzing homomorphisms between(viz., in the unitary case, endomorphisms of)their underlying algebrasand equally being a quite useful heuristic tool, manual applications of which are demonstratedwithin the framework of Lukasiewicz'finitely-valued logics, four-valued expansionsof Belnap's ``useful'' four-valued logic, their non-unitary three-valued extensions, unitary inferentially consistent non-classical onesbeing well-known to be non-self-extensional, as well as unitary three-valueddisjunctive (in particular, implicative) logicswith subclassical negation (includingboth paraconsistent and paracomplete o