Results 161 to 170 of about 2,017 (178)
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Czechoslovak Mathematical Journal, 2002
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Czechoslovak Mathematical Journal, 1998
An \(MV\)-algebra \(\mathcal A\) constructed by means of an abelian lattice ordered group \(G\) with a strong unit (\(G\) is uniquely determined by \(\mathcal A\)) is called archimedean (or semisimple) if \(G\) is archimedean. A non-empty subset \(\{a_j\mid j\in J\}\) of \(\mathcal A\) is said to be orthogonal if \(a_i\wedge a_j=0\) for all distinct ...
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An \(MV\)-algebra \(\mathcal A\) constructed by means of an abelian lattice ordered group \(G\) with a strong unit (\(G\) is uniquely determined by \(\mathcal A\)) is called archimedean (or semisimple) if \(G\) is archimedean. A non-empty subset \(\{a_j\mid j\in J\}\) of \(\mathcal A\) is said to be orthogonal if \(a_i\wedge a_j=0\) for all distinct ...
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Czechoslovak Mathematical Journal, 2003
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Fundamenta Informaticae, 2006
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 Łukasiewicz logic and we prove a completeness theorem.
GERLA, BRUNELLA, I. LEUSTEAN
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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 Łukasiewicz logic and we prove a completeness theorem.
GERLA, BRUNELLA, I. LEUSTEAN
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2016
C.C. Chang introduced MV-algebras as algebraic models for \({\L }\)ukasiewicz logic to give its algebraic analysis [1] and proved completeness of \({\L }\)ukasiewicz logic with respect to the variety of all MV-algebras. We give the definition of MV-algebra given originally by C.C. Chang in [1].
Antonio Di Nola +2 more
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C.C. Chang introduced MV-algebras as algebraic models for \({\L }\)ukasiewicz logic to give its algebraic analysis [1] and proved completeness of \({\L }\)ukasiewicz logic with respect to the variety of all MV-algebras. We give the definition of MV-algebra given originally by C.C. Chang in [1].
Antonio Di Nola +2 more
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Fuzzy Sets and Systems, 2016
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Manuela Busaniche +2 more
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Manuela Busaniche +2 more
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Quasi-MV* algebras: a generalization of MV*-algebras
Soft Computing, 2022Yingying Jiang, Wenjuan Chen
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2000
Free algebras are universal objects: every n-generated MV-algebra A is a homomorphic image of the free MV-algebra Free n over n generators; if an equation is satisfied by Free n then the equation is automatically satisfied by all MV-algebras. As a consequence of the completeness theorem, Free n is easily described as an MV-algebra of piecewise linear ...
Roberto L. O. Cignoli +2 more
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Free algebras are universal objects: every n-generated MV-algebra A is a homomorphic image of the free MV-algebra Free n over n generators; if an equation is satisfied by Free n then the equation is automatically satisfied by all MV-algebras. As a consequence of the completeness theorem, Free n is easily described as an MV-algebra of piecewise linear ...
Roberto L. O. Cignoli +2 more
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2016
Local MV-algebras are MV-algebras with only one maximal ideal that, hence, contains all infinitesimal elements.
Antonio Di Nola +2 more
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Local MV-algebras are MV-algebras with only one maximal ideal that, hence, contains all infinitesimal elements.
Antonio Di Nola +2 more
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Studia Logica, 1996
The infinite-valued logic \(L_\infty\) (Lukasiewicz logic) was introduced as a generalization of classical logic. \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704)] introduced MV algebras in order to provide an algebraic proof of its completeness theorem.
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The infinite-valued logic \(L_\infty\) (Lukasiewicz logic) was introduced as a generalization of classical logic. \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704)] introduced MV algebras in order to provide an algebraic proof of its completeness theorem.
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