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Probability Measures in the Logic of Nilpotent Minimum

Stefano Aguzzoli & Brunella Gerla

Studia Logica 94 (2):151-176 (2010)

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Averaging the truth-value in łukasiewicz logic.Daniele Mundici - 1995 - Studia Logica 55 (1):113 - 127.details Chang's MV algebras are the algebras of the infinite-valued sentential calculus of ukasiewicz. We introduce finitely additive measures (called states) on MV algebras with the intent of capturing the notion of average degree of truth of a proposition. Since Boolean algebras coincide with idempotent MV algebras, states yield a generalization of finitely additive measures. Since MV algebras stand to Boolean algebras as AFC-algebras stand to commutative AFC-algebras, states are naturally related to noncommutativeC*-algebraic measures. Download Export citation Bookmark 32 citations
Free nilpotent minimum algebras.Manuela Busaniche - 2006 - Mathematical Logic Quarterly 52 (3):219-236.details In the present paper we give a description of the free algebra over an arbitrary set of generators in the variety of nilpotent minimum algebras. Such description is given in terms of a weak Boolean product of directly indecomposable algebras over the Boolean space corresponding to the Boolean subalgebra of the free NM-algebra. Download Export citation Bookmark 5 citations
De Finetti’s No-Dutch-Book Criterion for Gödel logic.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Studia Logica 90 (1):25-41.details We extend de Finetti's No-Dutch-Book Criterion to Gödel infinite-valued propositional logic. Download Export citation Bookmark 3 citations
On the structure of rotation-invariant semigroups.Sándor Jenei - 2003 - Archive for Mathematical Logic 42 (5):489-514.details We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows from their other axioms. Download Export citation Bookmark 18 citations
Computing coproducts of finitely presented Gödel algebras.Ottavio M. D’Antona & Vincenzo Marra - 2006 - Annals of Pure and Applied Logic 142 (1):202-211.details We obtain an algorithm to compute finite coproducts of finitely generated Gödel algebras, i.e. Heyting algebras satisfying the prelinearity axiom =1. We achieve this result using ordered partitions of finite sets as a key tool to investigate the category opposite to finitely generated Gödel algebras . We give two applications of our main result. We prove that finitely presented Gödel algebras have free products with amalgamation; and we easily obtain a recursive formula for the cardinality of the free Gödel algebra (...) Download Export citation Bookmark 6 citations

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