Commutative deductive systems of pseudo-BCK-algebras
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DOI: 10.1007/s00500-017-2623-6
Abstract: In this paper, we generalize the axiom systems given by M. Pałasiński and B. Woźniakowska for commutative BCK-algebras to the case of commutative pseudo-BCK-algebras. A characterization of commutative pseudo-BCK-algebras is also given. We define the… read more here.
Keywords: deductive systems; commutative deductive; systems pseudo; bck algebras ... See more keywords
On Fuzzy Deductive Systems of Hilbert Algebras
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DOI: 10.1155/2020/6910726
Abstract: In this paper, we study fuzzy deductive systems of Hilbert algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law. Several characterizations are obtained for fuzzy deductive systems generated by… read more here.
Keywords: class fuzzy; deductive systems; hilbert algebras; systems hilbert ... See more keywords
Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property
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DOI: 10.3390/axioms8030100
Abstract: Using the defined notion of the inference with multiply-conclusion rules, we show that in the logics enjoying the disjunction property, any derivable rule can be inferred from the single-conclusion rules and a single multiple-conclusion rule,… read more here.
Keywords: multiple conclusion; deductive systems; conclusion rules; conclusion ... See more keywords
Deductive Systems in Traditional and Modern Logic
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DOI: 10.3390/axioms9030108
Abstract: Since its inception, logic has studied the acceptable rules of reasoning, the rules that allow us to pass from certain statements, serving as premises or assumptions, to a statement taken as a conclusion [...] read more here.
Keywords: modern logic; traditional modern; systems traditional; deductive systems ... See more keywords