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Convergence with a fixed regulator in perfect MV-algebras

Ciungu L.

Demonstratio Mathematica

2008

Vol. 41, nr 1

1-10

MV-algebras were introduced by Chang as an algebraic counterpart of the Łukasiewicz infinite-valued logie. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian l-groups with strong unit. A. Di Nola and A. Lettieri established a categorical equivalence between the category of perfect MV-algebras and the category of abelian l-groups. In this paper we investigate the convergence with a fixed regulator in perfect MV-algebras using Di Nola-Lettieri functors. The main result of the paper states that every locally Archimedean MV-algebra has a unique v-Cauchy completion.

Similarity MV-algebras

Gerla B., Leustean I.

Fundamenta Informaticae

2006

Vol. 69, nr 3

287-300

Similarities are an extension of equivalence relations to a fuzzy context. In this paper we introduce the class of similarity MV-algebras obtained as a generalization of the variety of MV-algebras by adding a binary operator playing the role of similarity. We further introduce the similarity ukasiewicz logic and we prove a completeness theorem.

Distributive atomic efect algebras

Riečanová Z.

Demonstratio Mathematica

2003

Vol. 36, nr 2

247--259

Motivated by the use of fuzzy or unsharp quantum logics as carriers of probability measures there have been recently introduced effect algebras (D-posets). We extend a result by Greechie, Foulis and Pulmannova of finite distributive effect algebras to all Archimedean atomic distributive effect algebras. We show that every such an effect algebra is join and meet dense in a complete effect algebra being a direct product of finite chains and distributive diamonds. This proves that every such effect algebra has a MacNeille completion being again a distributive effect algebra and both these effect algebras are continuous lattices. Moreover, we show that every faithful or (o)-continuous state (probability) on such an effect algebra is a valuation, hence a subadditive state. Its existence is also proved. Finally, we prove that every complete atomic distributive effect algebra E is a homomorphic image of a complete modular atomic ortholattice regarded as effect algebra and E is an MV-effect algebra (MV-algebra) if and only if it is a homomorphic image of a Boolean algebra regarded as effect algebra.