Probabilities on Lukasiewicz-Moisil algebras (Q1818105)

In his paper: ``Averaging the truth-value in Łukasiewicz logic'' [Stud. Log. 55, No. 1, 113-127 (1995; Zbl 0836.03016)] the present reviewer introduced finitely additive measures on Chang's MV-algebras. The latter are the Lindenbaum algebras of the infinite-valued sentential calculus of Łukasiewicz, and also correspond to certain limits of finite-dimensional \(C^*\)-algebras. Under this correspondence, MV-algebraic finitely additive measures correspond to \(C^*\)-algebraic tracial states. The authors define a similar notion for \(n\)-valued Łukasiewicz-Moisil algebras, and investigate its basic properties. In particular, they prove for \(n\)-valued Łukasiewicz-Moisil algebras an extension theorem for continuous measures, originating from Boolean algebraic probability theory, which was also known to hold for all \(n\)-valued MV-algebras.