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• W2808113673 abstract "The so-called non-associative MV-algebras were introduced recently by the first author and J. Kühr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g., Botur and Halaš (Arch Math Log 48:243-255, 2009). Since implication is an important logical connective in practically every propositional logic, in the present paper we investigate the implication reducts of non-associative MV-algebras. We also determine their structures based on the underlying posets. The natural question when a poset with the greatest element equipped with sectional switching involutions can be organized into an implication NMV-algebra is solved. Moreover, congruence properties of the variety of implication NMV-algebras with, respectively, without zero are investigated. Analogously to classical propositional logic, we introduce a certain kind of Sheffer operation and we obtain a one-to-one correspondence between NMV-algebras and certain algebras built up by a Sheffer-like operation together with a unary operation." @default.
• W2808113673 created "2018-06-21" @default.
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• W2808113673 date "2018-06-15" @default.
• W2808113673 modified "2023-10-17" @default.
• W2808113673 title "Operations and structures derived from non-associative MV-algebras" @default.
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• W2808113673 doi "https://doi.org/10.1007/s00500-018-3309-4" @default.
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