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Invertible substitutions in logics with algebraic semantics equivalent to Product algebras
No full textProduct logic is considered one of the major truth-functional fuzzy propositional logics. Its semantics is given by the variety of Product algebras {mathbb{P}}. In the hierarchy of fuzzy logics based on left-continuous t-norms there are a few logics whose algebraic semantics are varieties categorically equivalent with {mathbb{P}}. For these logics we shall describe finitely generated free algebras and their group of automorphisms, that is, invertible substitutions
Averaging the Truth Value of Formulas in Gödel Logic
No full textLet L be a propositional mathematical fuzzy logic with the real unit interval [0, 1] as its set of truth values. Assume that L has an algebraic semantics given by a variety V of algebras. A finitely additive probability measure (or, state) over the free n-generated V-algebra provides an average value over all assignments of a formula with n many variables in L only if this measure is invariant with respect to automorphisms of the free algebra. In this paper we characterise the states that are invariant with respect to automorphisms of the free n-generated Gödel algebra
Many-valued logic: beyond algebraic semantics
No full textEditorial for the special issue on "Many-valued logic: beyond algebraic semantics
A note on minimal axiomatisations of some extensions of MTL
No full textThe rotation of the product t-norm provides the tool to show that Łukasiewicz logic cannot be axiomatised as an extension of MTL by means of any set of axioms with at most one variable. As a corollary, also BL cannot be axiomatised from MTL by means of single-variable axiom
Journal of Logic and Computation, special issue on "Applications of Topological Dualities to Measure Theory in Algebraic Many-Valued Logic"
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