BCK-algebras, introduced in the 1960s by Imai and Iséki [3], form a well-known class of algebras intensively studied in algebraic logic during the last decades. The reason of their introduction was practically twofold: they describe general properties of algebras of sets with the set subtraction as a binary operation, and secondly, they form a natural generalization of algebraic counterparts of...

Partial Boolean algebras (PBA’s) were introduced by Kochen and Specker as an algebraic model reflecting the mutual relationships among quantumphysical yes-no tests. The fact that not all pairs of tests are compatible was taken into special account. In this paper, we review PBA’s from two sides. First, we generalize the concept, taking into account also those yes-no tests which are based on unsh...

The relationship between MV-algebras and semirings was described by A. Di Nola and B. Gerla ([7]). Since commutative basic algebras are similar to MV-algebras up to associativity of the binary operation we try to get a similar relationship between commutative basic algebras and so-called near semirings and we show that this is possible. This means that associativity does not play an important r...

A multi-valued version of CTL (mv-CTL), where both the propositions and the accessibility relation are multi-valued taking values in a nite quasi-Boolean algebra, is deened. A translation from mv-CTL model checking to CTL model checking is investigated. First, the case where the elements of quasi-Boolean algebras are totally ordered is considered. Secondly, it is shown how to design a translati...

We give necessary and sufficient conditions for the first-order theory of a finitely presented abelian lattice-ordered group to be decidable. We also show that if the number of generators is at most 3, then elementary equivalence implies isomorphism. We deduce from our methods that the theory of the free MV -algebra on at least 2 generators is undecidable.

for a suitably locally convex multivariable *-polynomial V . Indeed, they were able to establish that such an SDE has a unique stationary distribution μV satisfying the Schwinger-Dyson equation μV ⊗ μV (∂iP ) = μV (DiV P ) where ∂i is the non-commutative partial difference quotient and Di is the cyclic partial derivative. By using the fact that they also had convergence in norm to this distribu...

The Archimedean property is one of the most beautiful axioms of the classical arithmetic and some of the methods of constructing the field of real numbers are based on this property. It is well-known that every Archimedean `-group is abelian and every pseudo-MV algebra is commutative. The aim of this paper is to introduce the Archimedean property for pseudo-MTL algebras and FLw-algebras. The ma...

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.

We present a uniform relational framework for developing proof systems for theories of manyvaluedness that may have the form of a logical system, of a class of algebra or of an information system. We outline a construction of proof systems for SHn logics, mv−algebras and many−valued information systems.