Skip to main content
SpringerLink
Log in

On Axiomatizing Shramko-Wansing’s Logic

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

This work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ t and ⊨ f , determined via truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN 3 as a twist-structure over the two-element Boolean algebra.

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. Belnap, N.D., ‘A useful four-valued logic’, in G. Epstein and M.J. Dunn, (eds.), Modern Uses of Multiple-Valued Logic, Oriel Press, 7–37, 1977.

  2. Belnap, N.D., ‘How computer should think’, in G.Ryle, (ed.), Contemporary Aspects of Philosophy, Oriel Press, 1977, 30–56.

  3. Chagrov A., Zakharyaschev M.: Modal logic. Clarendon Press, Oxford (1997)

    Google Scholar 

  4. Fidel, M.M., ‘An algebraic study of a propositional system of Nelson’, in Mathematical Logic, Proc. of the First Brasilian Conference, Campinas 1977, Lect. Notes Pure Appl. Math., 39, 99–117, 1978.

  5. Kracht M.: On extensions of intermediate logics by strong negation. Journal of Philosophical Logic 27, 49–73 (1998)

    Article  Google Scholar 

  6. Miura S.: A remark on the intersection of two logics. Nagoja Math. J. 26, 167–171 (1966)

    Google Scholar 

  7. Odintsov S.P.: Algebraic semantics for paraconsistent Nelson’s Logic. Journal of Logic and Computation 13, 453–468 (2003)

    Article  Google Scholar 

  8. Odintsov S.P.: Constructive negations and paraconsistency. Springer, Dordrecht (2008)

    Google Scholar 

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

    Article  Google Scholar 

  10. Shramko Y., Wansing H.: Hypercontradictions, generalized truth values, and logics of truth and falsehood. Journal of Logic, Language and Information 15, 403–424 (2006)

    Article  Google Scholar 

  11. Vakarelov D.: Notes on N-lattices and constructive logic with strong negation. Studia logica 36, 109–125 (1977)

    Article  Google Scholar 

  12. Wansing H., Shramko Y.: An note on two ways of defining a many-valued logic. In: Pelis, M. (eds) Logica Yearbook 2007, pp. 255–266. Filosofia, Prague (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Koptyug prosp. 4, 630090, Novosibirsk, Russia

    Sergei P. Odintsov

  2. Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia

    Sergei P. Odintsov

Authors
  1. Sergei P. Odintsov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergei P. Odintsov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Odintsov, S.P. On Axiomatizing Shramko-Wansing’s Logic. Stud Logica 91, 407–428 (2009). https://doi.org/10.1007/s11225-009-9181-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-009-9181-6

Keywords

Search

Navigation