Averaging the truth-value in łukasiewicz logic

Studia Logica 55 (1):113 - 127 (1995)

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.
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DOI 10.1007/BF01053035
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References found in this work BETA

An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
A Theorem About Infinite-Valued Sentential Logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
Model Theory.C. C. Chang & H. J. Keisler - 1976 - Journal of Symbolic Logic 41 (3):697-699.

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State-Morphism MV-Algebras.Antonio Di Nola & Anatolij Dvurečenskij - 2009 - Annals of Pure and Applied Logic 161 (2):161-173.
Representation and Extension of States on MV-Algebras.TomአKroupa - 2005 - Archive for Mathematical Logic 45 (4):381-392.
Subdirectly Irreducible State-Morphism BL-Algebras.Anatolij Dvurečenskij - 2011 - Archive for Mathematical Logic 50 (1-2):145-160.

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