Structural Rules for Multi-valued Logics
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We study structural rules in the context of multi-valued logics with finitely-many truth-values. We first extend Gentzen’s traditional structural rules to a multi-valued logic context; in addition, we propos some novel structural rules, fitting only multi-valued logics. Then, we propose a novel definition, namely, structural rules completeness of a collection of structural rules, requiring derivability of the restriction of consequence to atomic formulas by structural rules only. The restriction to atomic formulas relieves the need to concern logical rules in the derivation.
KeywordsStructural rules Multi-valued logics Structural rules completeness
Mathematics Subject ClassificationPrimary 03F03 Secondary 03B22 03A02
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