Displaying similar documents to “Enriched MV-algebras.”

Directoids with sectionally antitone involutions and skew MV-algebras

Ivan Chajda, Miroslav Kolařík (2007)

Mathematica Bohemica

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It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.

The σ-complete MV-algebras which have enough states

Antonio Di Nola, Mirko Navara (2005)

Colloquium Mathematicae

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We characterize Łukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Łukasiewicz t-norm with countably many arguments. As a tool, we introduce σ-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of σ-complete MV-algebras which are isomorphic to Łukasiewicz tribes.

A spectral theorem for σ MV-algebras

Sylvia Pulmannová (2005)

Kybernetika

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MV-algebras were introduced by Chang, 1958 as algebraic bases for multi-valued logic. MV stands for “multi-valued" and MV algebras have already occupied an important place in the realm of nonstandard (mathematical) logic applied in several fields including cybernetics. In the present paper, using the Loomis–Sikorski theorem for σ -MV-algebras, we prove that, with every element a in a σ -MV algebra M , a spectral measure (i. e. an observable) Λ a : ℬ ( [ 0 , 1 ] ) → ℬ ( M ) can be associated, where ℬ ( M ) denotes the Boolean...