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The paper is a contribution both to the theoretical foundations and to theactual construction of efficient automatizable proof procedures fornon-classical logics. We focus here on the case of finite-valued logics, andexhibit: (i) a mechanism for producing a classic-like description of them interms of an effective variety of bivalent semantics; (ii) a mechanism forextracting, from the bivalent semantics so obtained, uniform(classically-labeled) cut-free standard analytic tableaux with possiblybranching invertible rules and paired with proof strategies designed toguarantee termination of the associated proof procedure; (iii) a mechanism toalso provide, for the same logics, uniform cut-based tableau systems withlinear rules. The latter tableau systems are shown to be adequate even whenrestricted to analytic cuts, and they are also shown to polynomially simulatetruth-tables, a feature that is not enjoyed by the former standard type oftableau systems (not even in the 2-valued case). The results are based onuseful generalizations of the notions of analyticity and compositionality, andillustrate a theory that applies to many other classes of non-classical logics.

Bivalent semantics, generalized compositionality and analytic classic-like tableaux for finite-valued logics