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Completeness with respect to a chain and universal models in fuzzy logic

Franco Montagna

Archive for Mathematical Logic 50 (1-2):161-183 (2011)

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Trakhtenbrot Theorem and First-Order Axiomatic Extensions of MTL.Matteo Bianchi & Franco Montagna - 2015 - Studia Logica 103 (6):1163-1181.details In 1950, B.A. Trakhtenbrot showed that the set of first-order tautologies associated to finite models is not recursively enumerable. In 1999, P. Hájek generalized this result to the first-order versions of Łukasiewicz, Gödel and Product logics, w.r.t. their standard algebras. In this paper we extend the analysis to the first-order versions of axiomatic extensions of MTL. Our main result is the following. Let \ be a class of MTL-chains. Then the set of all first-order tautologies associated to the finite models (...) Download Export citation Bookmark 1 citation
The Variety Generated by all the Ordinal Sums of Perfect MV-Chains.Matteo Bianchi - 2013 - Studia Logica 101 (1):11-29.details We present the logic BLChang, an axiomatic extension of BL (see [23]) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of BLChang-algebras will be strictly connected to the one generated by Chang’s MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new (...) Download Export citation Bookmark

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