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• W182942587 abstract "This dissertation is focused on an algebraic approach of some many-valued generalizations of modal logics. The starting point is the definition of the [0, 1]-valued and the Łn-valued Kripke models, where [0, 1] denotes the well known MV-algebra and Łn its finite subalgebra {0, 1 n , . . . , n−1 n , 1} for any positive integer n. Two types of structures are used to define validity of formulas: the class of L-frames and the class of Łn-valued L-frames. The latter structures are L-frames in which we specify in each world u the set Łm (where m is a divisor of n) of the possible truth values of the formulas in u. These two classes of structures define two distinct notions of validity. We use these notions to study the problem of definability of classes of structures with modal formulas. We obtain for these two classes an equivalent of the Goldblatt Thomason theorem. We are able to consider completeness problems with respect to these relational semantics thanks to the connections between relational and algebraic semantics. Our strongest results are about Łn-valued logic. We are indeed able to apply and develop algebraic tools (namely, canonical and strong canonical extensions) that allow to generate complete Łn-valued logics." @default.
• W182942587 created "2016-06-24" @default.
• W182942587 creator A5019880686 @default.
• W182942587 date "2009-01-01" @default.
• W182942587 modified "2023-09-26" @default.
• W182942587 title "Algebraic approach to modal extensions of Łukasiewicz logics" @default.
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• W182942587 hasPublicationYear "2009" @default.
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