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Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property

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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… Click to show full 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, which represents the disjunction property. Also, the conversion algorithm of single- and multiple-conclusion deductive systems into each other is studied.

Keywords: multiple conclusion; deductive systems; conclusion rules; conclusion; disjunction property

Journal Title: Axioms
Year Published: 2019

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