Skip to main content
Log in

Gentzenization of Trilattice Logics

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

Sequent calculi for trilattice logics, including those that are determined by the truth entailment, the falsity entailment and their intersection, are given. This partly answers the problems in Shramko-Wansing (J Philos Logic 34:121–153, 2005).

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

Access this article

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. Kamide N., Wansing H.: Sequent calculi for some trilattice logics. The Review of Symbolic Logic 2, 374–395 (2009)

    Article  Google Scholar 

  2. Kamide N., Wansing H.: Completeness and cut-elimination theorems for trilattice logics. Annals of Pure and Applied Logic 162, 816–835 (2011)

    Article  Google Scholar 

  3. Odintsov S. P.: On axiomatizing Shramko-Wansing’s logic. Studia Logica 91, 407–428 (2009)

    Article  Google Scholar 

  4. Odintsov S.P., Wansing H.: The logic of generalized truth values and the logic of bilattices. Studia Logica 103, 91–112 (2015)

    Article  Google Scholar 

  5. Shramko Y., Wansing H.: Some usuful 16-valued logics: How a computer network should think. Journal of Philosophical Logic 34, 121–153 (2005)

    Article  Google Scholar 

  6. Takano M.: Sequent calculus for the intersection of LK and the reversed. Far East Journal of Mathematical Sciences 68, 297–305 (2012)

    Google Scholar 

  7. Takeuti G.: Proof Theory. Amsterdam, North-Holland (1975)

    Google Scholar 

  8. Wansing H.: The power of Belnap: Sequent systems for SIXTEEN 3. Journal of Philosophical Logic 39, 369–393 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mitio Takano.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Takano, M. Gentzenization of Trilattice Logics. Stud Logica 104, 917–929 (2016). https://doi.org/10.1007/s11225-016-9658-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-016-9658-z

Keywords

Navigation