Skip to main content
SpringerLink
Log in

Symbolic Models for Single-Conclusion Proof Logics

  • Conference paper
Computer Science – Theory and Applications (CSR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6072))

Included in the following conference series:

Abstract

Symbolic semantics for logics of proofs based on Mkrtychev models covers the the case of multi-conclusion proof logics. We propose symbolic models for single-conclusion proof logics (FLP and its extensions). The corresponding soundness and completeness theorems are proven. The developed symbolic model technique is used to establish the consistency of contexts required for proof internalization. In particular, we construct an extension of FLP that enjoys the strong proof internalization property with empty context.

The research described in this paper was partially supported by grants RFBR 08-01-00399, 06-01-72554 and INTAS 05-1000008-8144.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Artemov, S., Straßen, T.: Functionality in the basic logic of proofs. Technical Report IAM 92-004, University of Bern (1993)

    Google Scholar 

  2. Artemov, S.: Operational modal logic. Technical Report MSI 95–29, Cornell University (1995)

    Google Scholar 

  3. Artemov, S., Krupski, V.: Data storage interpretation of labeled modal logic. Annals of Pure and Applied Logic 78(1-3), 57–71 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Artemov, S.: Explicit provability and constructive semantics. Bulletin of Symbolic Logic 7(1), 1–36 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Artemov, S., Yavorskaya (Sidon), T.: On first order logic of proofs. Moscow Mathemetical Journal 1(4), 475–490 (2001)

    MATH  Google Scholar 

  6. Artemov, S.N.: Kolmogorov and Gödel’s approach to intuitionistic logic: current developements. Russian Mathematical Surveys 59(2), 203–229 (2004)

    Article  MathSciNet  Google Scholar 

  7. Artemov, S., Beklemishev, L.: Provability logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 13, pp. 189–360. Springer, Heidelberg (2005)

    Google Scholar 

  8. Artemov, S., Nogina, E.: Introducing justification into epistemic logic. Journal of Logic and Computation 15(6), 1059–1073 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fitting, M.: The logic of proofs, semantically. Annals of Pure and Applied Logic 132(1), 1–25 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Krupski, V.: Operational logic of proofs with functionality condition on proof predicate. In: Adian, S., Nerode, A. (eds.) LFCS 1997. LNCS, vol. 1234, pp. 167–177. Springer, Heidelberg (1997)

    Google Scholar 

  11. Krupski, V.: The single-conclusion proof logic and inference rules specification. Annals of Pure and Applied Logic 113(1-3), 181–206 (2001)

    Article  MathSciNet  Google Scholar 

  12. Krupski, V.: Reference constructions in the single-conclusion proof logic. Journal of Logic and Computation 16(5), 645–661 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Krupski, V.: Referential logic of proofs. Theoretical Computer Science 357(1-3), 143–166 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kuznets, R.: On the complexity of explicit modal logics. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 371–383. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Mkrtychev, A.: Models for the Logic of Proofs. In: Adian, S., Nerode, A. (eds.) LFCS 1997. LNCS, vol. 1234, pp. 266–275. Springer, Heidelberg (1997)

    Google Scholar 

  16. Rubtsova, N.: On realization of S5-modality by evidence terms. Journal of Logic and Computation 16(5), 671–684 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  17. Rubtsova, N.M.: Logic of Proofs with substitution. Mathematical Notes 82(5-6), 816–826 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Yavorskaya (Sidon), T.: Negative operations on proofs and labels. Journal of Logic and Computation 15(4), 517–537 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  19. Yavorskaya (Sidon), T., Rubtsova, N.: Operations on proofs and labels. Journal of Applied Non-Classical Logics 17(3), 283–316 (2007)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119992, Russia

    Vladimir N. Krupski

Authors
  1. Vladimir N. Krupski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Theoretical Cybernetics, Kazan State University, 420008, Kazan, Russia

    Farid Ablayev

  2. Institut für Informatik, Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Krupski, V.N. (2010). Symbolic Models for Single-Conclusion Proof Logics . In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13182-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13181-3

  • Online ISBN: 978-3-642-13182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation