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Structural Rules for Multi-valued Logics

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Abstract

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.

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References

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Authors and Affiliations

  1. Computer Science Department, Technion-IIT, Haifa, Israel

    Nissim Francez & Michael Kaminski

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  1. Nissim Francez
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  2. Michael Kaminski
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Correspondence to Nissim Francez.

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A talk based on this paper was presented at the second Substructural logics: semantics, proof theory, and applications (SYSMICS) conference, Vienna, February 2018.

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Francez, N., Kaminski, M. Structural Rules for Multi-valued Logics. Log. Univers. 13, 65–75 (2019). https://doi.org/10.1007/s11787-019-00219-z

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  • DOI: https://doi.org/10.1007/s11787-019-00219-z

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