Skip to main content
SpringerLink
Log in

Semi-intuitionistic Logic with Strong Negation

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.

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. Cornejo, J. M., Semi-intuitionistic logic, Studia Logica 98(1–2):9–25, 2011.

    Article  Google Scholar 

  2. Cornejo, J. M., and I. D. Viglizzo, On some semi-intuitionistic logics, Studia Logica 103(2):303–344, 2015.

    Article  Google Scholar 

  3. Cornejo, J. M., and I. D. Viglizzo, Semi-Nelson algebras, Order 2016. DOI:10.1007/s11083-016-9416-x.

  4. Cornejo, J. M., and I. D. Viglizzo, Proofs of Some Propositions of the Semi-intuitionistic Logic with Strong Negation. Informe Técnico Interno 103, Instituto de Matemática de Bahía Blanca, Universidad Nacional del Sur-CONICET, 2017. http://inmabb-conicet.gob.ar/publicaciones/iti/iti103.pdf.

  5. Fitting, M. C., Intuitionistic Logic, Model Theory and Forcing, Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., Amsterdam, 1969.

    Google Scholar 

  6. Font, J. M., R. Jansana, and D. Pigozzi, A survey of abstract algebraic logic, Studia Logica 74(1–2):13–97, 2003. Abstract algebraic logic, Part II (Barcelona, 1997).

  7. Monteiro, A., and L. Monteiro, Axiomes indépendants pour les algèbres de Nelson, de Łukasiewicz trivalentes, de De Morgan et de Kleene, in Unpublished Papers, I, vol 40 of Notas Lógica Mat., Universidad Nacional del Sur, Bahía Blanca, 1996, p 13.

  8. Nelson, D., Constructible falsity, The Journal of Symbolic Logic 14:16–26, 1949.

    Article  Google Scholar 

  9. Rasiowa, H., \({\cal{N}}\)-lattices and constructive logic with strong negation, Fundamenta Mathematicae 46:61–80, 1958.

  10. Rasiowa, H., An Algebraic Approach to Non-classical Logics, Vol. 78, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1974.

    Book  Google Scholar 

  11. Sankappanavar, H. P., Semi-Heyting algebras, American Mathematical Society Abstracts 6(1):13, 1985.

    Google Scholar 

  12. Sankappanavar, H. P., Semi-Heyting algebras: An abstraction from Heyting algebras, in Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress (Spanish), Actas Congreso “Dr. Antonio A. R. Monteiro”, Universidad Nacional del Sur, Bahía Blanca, 2008, pp. 33–66.

  13. Vakarelov, D., Notes on \({\cal{N}}\)-lattices and constructive logic with strong negation, Studia Logica 36(1–2):109–125, 1977.

    Article  Google Scholar 

  14. Viglizzo, I., Álgebras de Nelson. Instituto de Matemática de Bahía Blanca, Universidad Nacional del Sur. Magister dissertation in Mathematics, 1999. https://sites.google.com/site/viglizzo/viglizzo99nelson.

Download references

Acknowledgements

We gratefully acknowledge the constructive comments and corrections offered by the referees. This work was partially supported by CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina).

Author information

Authors and Affiliations

  1. Instituto de Matemática de Bahía Blanca (INMABB), Universidad Nacional del Sur-CONICET, Bahía Blanca, Argentina

    Juan Manuel Cornejo

  2. Departamento de Matemática, Universidad Nacional del Sur (UNS), Bahía Blanca, Argentina

    Ignacio Viglizzo

Authors
  1. Juan Manuel Cornejo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ignacio Viglizzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ignacio Viglizzo.

Additional information

Presented by Richmond Thomason

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cornejo, J.M., Viglizzo, I. Semi-intuitionistic Logic with Strong Negation. Stud Logica 106, 281–293 (2018). https://doi.org/10.1007/s11225-017-9737-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-017-9737-9

Keywords

Search

Navigation