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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C. C. Chang & H. J. Keisler (1976). Model Theory. Journal of Symbolic Logic 41 (3):697-699.

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