7 found
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  1.  6
    The Free N-Generated BL-Algebra.Stefano Aguzzoli & Simone Bova - 2010 - Annals of Pure and Applied Logic 161 (9):1144-1170.
    For each integer n≥0, we provide an explicit functional characterization of the free n-generated BL-algebra, together with an explicit construction of the corresponding normal forms.
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  2.  26
    De Finetti's No-Dutch-Book Criterion for Gödel Logic.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Studia Logica 90 (1):25 - 41.
    We extend de Finetti’s No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.
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  3.  37
    A Temporal Semantics for Basic Logic.Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra - 2009 - Studia Logica 92 (2):147-162.
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...)
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  4.  33
    Probability Measures in the Logic of Nilpotent Minimum.Stefano Aguzzoli & Brunella Gerla - 2010 - Studia Logica 94 (2):151-176.
    We axiomatize the notion of state over finitely generated free NM-algebras, the Lindenbaum algebras of pure Nilpotent Minimum logic. We show that states over the free n -generated NM-algebra exactly correspond to integrals of elements of with respect to Borel probability measures.
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  5.  30
    Finiteness in Infinite-Valued Łukasiewicz Logic.Stefano Aguzzoli & Agata Ciabattoni - 2000 - Journal of Logic, Language and Information 9 (1):5-29.
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same (...)
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  6.  5
    De Finetti’s No-Dutch-Book Criterion for Gödel Logic.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Studia Logica 90 (1):25-41.
    We extend de Finetti's No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.
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  7.  2
    Gödel Algebras Free Over Finite Distributive Lattices.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Annals of Pure and Applied Logic 155 (3):183-193.
    Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom =. In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest.
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