Skip to main content
SpringerLink
Log in

Structural Rules for Multi-valued Logics

  • Published:
Logica Universalis Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baaz, M., Fermüler, C.G., Zach, R.: Systematic construction of natural deduction systems for many-valued logics. In: Proceedings of the 23rd International Symposium on Multiple Valued Logics, Sacramento, CA, May 1993, pp. 208–213. IEEE press, Los Alamitos, (1993)

  2. Francez, N., Kaminski, M.: On poly-logistic natural-deduction for finitely-valued propositional logics. J. Appl. Logic (to appear), 2019. Presented at ISRALOG17, Haifa, (October 2017)

  3. Gentzen, G.: Investigations into logical deduction. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen, pp. 68–131. North-Holland, Amsterdam (1935). English translation of the 1935 paper in German

  4. Kaminski, M., Francez, N.: Calculi for multi-valued logics. (2018) (in preparation)

  5. Panti, Giovanni: Multi-valued logics. In: Gabbay, Dov, Smets, Philippe (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 25–74. Kluwer, Dordrecht (1998)

    Google Scholar 

  6. Wintein, Stefan, Muskens, Reinhard: Nothing but the truth. J. Philos. Logic 45(4), 451–465 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Nissim Francez & Michael Kaminski

Authors
  1. Nissim Francez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Kaminski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nissim Francez.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

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

Keywords

Mathematics Subject Classification

Search

Navigation