## Averaging the truth-value in Łukasiewicz logic.(English)Zbl 0836.03016

Summary: 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 AF $$C^*$$-algebras stand to commutative AF $$C^*$$-algebras, states are naturally related to noncommutative $$C^*$$-algebraic measures.

### MSC:

 03B50 Many-valued logic 03G25 Other algebras related to logic 06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects) 46L89 Other “noncommutative” mathematics based on $$C^*$$-algebra theory
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### References:

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