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The non-commutative counterpart of the well-known Łukasiewicz propositional logic is developed, in strong connection with the algebraic theory of psMV-algebras. An extension by a new unary logical connective is also considered and a stronger completeness result is proved for this system. The system PL presented in this paper can be seen as the… (More)
We develop the general theory of RMV-algebras, which are essentially unit intervals in Riesz spaces with strong unit. Since the variety of RMV-algebras is generated by [0, 1], we get an equational characterization of the real product on [0,1] interpreted as scalar multiplication.
The state theory on MV-algebras is a generalization of Boolean probability theory and is a counterpart of the theory of states defined on lattice-ordered groups. We first investigate the metric space naturally associated to an MV-algebra with a state. The metric completion of an MV-algebra is defined and characterized in relation with the geometric… (More)
We define a concept of probability on an n-valued Lukasiewicz-Moisil algebra and we present some basic properties. The main result is an extension theorem for continuous probabilities, which is already known for probabilities defined on Boolean algebras and MV-algebras. © 1998 Elsevier Science Inc. All rights reserved.