Skip to main content
SpringerLink
Log in

A proof-search procedure for intuitionistic propositional logic

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

A sequent root-first proof-search procedure for intuitionistic propositional logic is presented. The procedure is obtained from modified intuitionistic multi-succedent and classical sequent calculi, making use of Glivenko’s Theorem. We prove that a sequent is derivable in a standard intuitionistic multi-succedent calculus if and only if the corresponding prefixed-sequent is derivable in the procedure.

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. Alonderis R.: Glivenko classes of sequents for propositional star-free likelihood logic. Logic J. IGPL 15(1), 1–19 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Galmiche, D., Méry, D.: A connection-based characterization of bi-intuitionistic validity. In: CADE, pp. 268–282 (2011)

  3. Glivenko, V.: Sur quelques points de la logique de M. Brouwer. Bull. cl. sci. Acad. Roy. Belg., ser 5, 15, 183–188 (1929)

    Google Scholar 

  4. Negri S., von Plato J.: Structural Proof Theory. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  5. Orevkov V.: On Glivenko classes of sequents. Trudy Matematicheskogo Instituta imeni V. A. Steklova 98, 131–154 (1968)

    MathSciNet  MATH  Google Scholar 

  6. Otten, J.: A connection based proof method for intuitionistic logic. In: TABLEAUX, pp. 122–137 (1995)

  7. Otten, J., Kreitz, Ch.: A uniform proof procedure for classical and non-classical logics. KI, pp. 307–319 (1996)

  8. Otten, J.: leanCoP 2.0 and ileanCoP 1.2: high performance lean theorem proving in classical and intuitionistic logic (system descriptions). In: IJCAR, pp. 283–291 (2008)

  9. Ritter E., Pym D.J., Wallen L.A.: On the intuitionistic force of classical search. Theor. Comput. Sci 232(1–2), 299–333 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Troelstra A.S., Schwichtenberg H.: Basic Proof Theory, 2nd edn. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  11. Waaler, A.: Connections in nonclassical logics. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 1487–1578. Elsevier Science Publishers B.V., Amsterdam (2001)

  12. Wallen L.A.: Automated Proof Search In Non-classical Logics—Efficient Matrix Proof Methods for Modal and Intuitionistic Logics. MIT Press, Cambridge (1990)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, 2600, Vilnius, Lithuania

    R. Alonderis

Authors
  1. R. Alonderis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Alonderis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alonderis, R. A proof-search procedure for intuitionistic propositional logic. Arch. Math. Logic 52, 759–778 (2013). https://doi.org/10.1007/s00153-013-0342-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-013-0342-y

Keywords

Mathematics Subject Classification

Search

Navigation