Abstract
Chang's MV algebras are the algebras of the infinite-valued sentential calculus of Łukasiewicz. 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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Mundici, D. Averaging the truth-value in Łukasiewicz logic. Stud Logica 55, 113–127 (1995). https://doi.org/10.1007/BF01053035
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DOI: https://doi.org/10.1007/BF01053035