Skip to main content
SpringerLink
Log in
Book cover

Australian Joint Conference on Artificial Intelligence

AI 1998: Advanced Topics in Artificial Intelligence pp 107–118Cite as

A mechanisation of classical modal tense logics using isabelle

  • Scientific Track
  • Conference paper
  • First Online:

  • 177 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1502))

Abstract

We present an implementation of an interactive theorem prover for the basic tense logic K t , and many of its extensions, using the generic proof assistant Isabelle. The novelty of the implementation is that we use a Display Logic formalism of K t as opposed to a traditional Gentzen system. The prover is intended to assist in meta-theoretical studies of tense logics rather than to be a fast theorem prover. Since Display Logic is a generic way to capture multi-modal logics, our implementation can be trivially extended to handle the multi-modal logics of “time”, “knowledge”, “intentions”, “desires” and “beliefs” which are used in Artificial Intelligence research.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A R Anderson and N D Belnap. Entailment: The Logic of Relevance and Necessity, 1. Princeton University Press, Princeton, USA, 1975.

    Google Scholar 

  2. N D Belnap. Display logic. J. of Philosophical Logic, 11:375–417, 1982.

    MATH  MathSciNet  Google Scholar 

  3. J Barwise, D Gabbay, and C Hartonas. On the logic of information flow. Bulletin of the IGPL, 3(1):7–49, 1995.

    MATH  MathSciNet  Google Scholar 

  4. L Farinas Del Cerro. A simple deduction method for modal logic. Information Processing Letters, 14(2):49–51, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  5. J E Dawson. Simulating term-rewriting in LPF and in display logic. (submitted), Automated Reasoning Project, 1997.

    Google Scholar 

  6. F Debart, P Enjalbert, and M Lescot. Multi-modal logic programming using r=equational and order-sorted logic. Technical Report 90-3, 1990.

    Google Scholar 

  7. J E Dawson and R Goré. A mechanised proof system for relation algebra using display logic. (submitted), Automated Reasoning Project, 1997.

    Google Scholar 

  8. S Demri and R Goré. Cut-free display calculi for nominal tense logics. (submitted), Automated Reasoning Project, 1998.

    Google Scholar 

  9. K Došen and P Schroeder-Heister, editors. Substructural Logics. Studies in Logic and Computation. Oxford University Press, 1993.

    Google Scholar 

  10. R Fagin, J Halpern, Y Moses, and M Vardi. Reasoning about Knowledge. The MIT Press, 1995.

    Google Scholar 

  11. J-Y Girard. Linear logic. Theoretical Computer Science, 50:1–102, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  12. R Goré. Cut-free display calculi for relation algebras. In D van Dalen and M Bezem, editors, CSL96, LNCS 1258, 198–210. Springer, 1997.

    Google Scholar 

  13. R Goré. Substructural logics on display. Logic Journal of the IGPL, 6(3):451–504, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  14. G E Hughes and M J Cresswell. A New Introduction To Modal Logic. Routledge, 1996.

    Google Scholar 

  15. A Heuerding, M Seyfried, and H Zimmermann. Efficient loop-check for backward proof search in some non-classical logics. In Tableaux 96, LNAI 1071, 210–225. Springer, 1996.

    Google Scholar 

  16. M Kracht. Power and weakness of the modal display calculus. In H Wansing, editor, Proof Theory of Modal Logics, 92–121. Kluwer, 1996.

    Google Scholar 

  17. M Wooldridge M Fisher and C Dixon. A resolution-based proof method for temporal logics of knowledge and belief. In D Gabbay and J-J Ohlbach, editors, Proceedings of FAPR’96, 178–192. Springer-Verlag, 1996.

    Google Scholar 

  18. H-J Ohlbach. A resolution calculus for modal logics. In CADE-9, LNCS 310, 500–516. Springer-Verlag, 1988.

    Google Scholar 

  19. L C Paulson. Isabelle: The next 700 theorem provers. In P Odifreddi, editor, Logic and Computer Science, 361–385. Academic Press, 1990.

    Google Scholar 

  20. V Pratt. Action logic and pure induction. In JELIA 90, LNCS 478, 97–120. Springer-Verlag, 1991.

    Google Scholar 

  21. G Restall. Displaying and deciding substructural logics I: logics with contraposition. Journal of Philosophical Logic, to appear, 1998.

    Google Scholar 

  22. L A Wallen. Automated Deduction in Nonclassical Logics: Efficient Matrix Proof Methods for Modal and Intuitionistic Logics. MIT Press, 1989.

    Google Scholar 

  23. H Wansing. Sequent calculi for normal modal propositional logics. Journal of Logic and Computation, 4:125–142, 1994.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Automated Reasoning Project and Department of Computer Science, Australian National University, 0200, Canberra

    Jeremy E Dawson & Rajeev Goré

Authors
  1. Jeremy E Dawson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajeev Goré
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Grigoris Antoniou John Slaney

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dawson, J.E., Goré, R. (1998). A mechanisation of classical modal tense logics using isabelle. In: Antoniou, G., Slaney, J. (eds) Advanced Topics in Artificial Intelligence. AI 1998. Lecture Notes in Computer Science, vol 1502. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095045

Download citation

  • DOI: https://doi.org/10.1007/BFb0095045

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65138-3

  • Online ISBN: 978-3-540-49561-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation