BL-algebras and quantum structures
Thomas Vetterlein (2004)
Mathematica Slovaca
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Thomas Vetterlein (2004)
Mathematica Slovaca
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Hector Freytes (2004)
Czechoslovak Mathematical Journal
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The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder...
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 -MV-algebras, we prove that, with every element in a -MV algebra , a spectral measure (i. e. an observable) can be associated, where denotes the Boolean...
Francesc Esteva, Lluis Godo (1999)
Mathware and Soft Computing
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In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law. ...
Ivan Chajda (2009)
Discussiones Mathematicae - General Algebra and Applications
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The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
Don Pigozzi, Antonino Salibra (1993)
Banach Center Publications
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The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.