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Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1617))

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Abstract

We define sequent-style calculi for nominal tense logics characterized by classes of modal frames that are first-order definable by certain П 01 -formulae and П 02 -formulae. The calculi are based on d’Agostino and Mondadori’s calculus KE and therefore they admit a restricted cutrule that is not eliminable. A nice computational property of the restriction is, for instance, that at any stage of the proof, only a finite number of potential cut-formulae needs to be taken under consideration. Although restrictions on the proof search (preserving completeness) are given in the paper and most of them are theoretically appealing, the use of those calculi for mechanization is however doubtful. Indeed, we present sequent calculi for fragments of classical logic that are syntactic variants of the sequent calculi for the nominal tense logics.

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References

  1. M. Baldoni. Normal Multimodal Logics: Automated Deduction and Logic Programming. PhD thesis, Università degli Studi di Torino, 1998.

    Google Scholar 

  2. J. van Benthem. Modal logic and classical logic. Bibliopolis, 1983.

    Google Scholar 

  3. B. Beckert and R. Goré. Free variable tableaux for propositional modal logics. In TABLEAUX’97, pages 91–106. LNAI 1227, Springer, 1997.

    Google Scholar 

  4. N. Bonnette and R. Goré. A labelled sequent systems for tense logic Kt. In Australian Joint Conference of Articifial Intelligence, pages 71–82. LNAI 1502, Springer, 1998.

    Google Scholar 

  5. P. Blackburn. Nominal tense logic. Notre Dame Journal of Formal Logic, 34(1):56–83, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Blackburn. Internalizing labeled deduction. Technical Report 102, Computerlinguistik, Universität des Saarlandes, 1998.

    Google Scholar 

  7. D. Basin, S. Matthews, and L. Viganò. Labelled propositional modal logics: Theory and practice. J. of Logic and Computation, 7(6):685–717, 1997.

    Article  MATH  Google Scholar 

  8. D. Basin, S. Matthews, and L. Viganò. Natural deduction for non-classical logics. Studia Logica, 60(1):119–160, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  9. G. Boolos. Don’t eliminate cut. J. of Philosophical Logic, 13:373–378, 1984.

    MATH  MathSciNet  Google Scholar 

  10. M. Castilho, L. Fariñas del Cerro, O. Gasquet, and A. Herzig. Modal tableaux with propagation rules and structural rules. Fundamenta Informaticae, 32(3/4):281–297 1997.

    MATH  MathSciNet  Google Scholar 

  11. M. d’Agostino. Investigations into the complexity of some propositional calculi. PhD thesis, Oxford University Computing Laboratory, 1990.

    Google Scholar 

  12. S. Demri and R. Goré. Cut-free display calculi for nominal tense logics. In this volume, 1999.

    Google Scholar 

  13. M. d’Agostino and M. Mondadori. The taming of the cut. Classical refutations with analytic cut. J. of Logic and Computation, 4(3):285–319, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Fitting. Proof methods for modal and intuitionistic logics. D. Reidel Publishing Co., 1983.

    Google Scholar 

  15. D. Gabbay. Labelled Deductive Systems. Oxford University Press, 1996.

    Google Scholar 

  16. I. Gent. Analytic proof systems for classical and modal logics of restricted quantification. PhD thesis, University of Warwick, 1992.

    Google Scholar 

  17. G. Gargov and V. Goranko. Modal logic with names. J. of Philosophical Logic, 22(6):607–636, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  18. H. Ganzinger, U. Hustadt, and R. Meyer and C. Schmidt. A resolution-based decision procedure for extensions of K4. In 2nd Workshop on Advances in Modal Logic, 1998. to appear.

    Google Scholar 

  19. R Goré. Tableaux methods for modal and temporal logics. In Handbook of Tableaux Methods. Kluwer, Dordrecht, 1999. to appear.

    Google Scholar 

  20. G. Governatori. Labelled tableaux for multi-modal logics. In TABLEAUX-4, pages 79–94. LNAI 918, Springer, 1995.

    Google Scholar 

  21. A. Heuerding. Sequent Calculi for Proof Search in Some Modal Logics. PhD thesis, University of Bern, 1998.

    Google Scholar 

  22. J. Hudelmaier. Improved decision procedures for the modal logics K, KT and S4. In CSL’95, pages 320–334. LNCS 1092, Springer, 1996.

    Google Scholar 

  23. B. Konikowska. A logic for reasoning about relative similarity. Studia Logica, 58(1):185–226, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  24. M. Kracht. Power and weakness of the modal display calculus. In H. Wansing, editor, Proof theory of modal logic, pages 93–121. Kluwer Academic Publishers, 1996.

    Google Scholar 

  25. S. Kripke. Semantical analysis of modal logic I: normal modal propositional calculi. Zeitschrift für Mathematik Logik und Grundlagen der Mathematik, 9:67–96, 1963.

    Article  MATH  MathSciNet  Google Scholar 

  26. F. Massacci. Strongly analytic tableaux for normal modal logics. In CADE-12, pages 723–737. Springer, LNAI 814, 1994.

    Google Scholar 

  27. Z. Ognjanović. A tableau-like proof procedure for normal modal logics. TCS, 129:167–186, 1994.

    Article  MATH  Google Scholar 

  28. A. Prior. Time and Modality. Clarendon Press, Oxford, 1957.

    MATH  Google Scholar 

  29. N. Rescher and A. Urquhart. Temporal Logic. Springer-Verlag, 1971.

    Google Scholar 

  30. A. Russo. Modal logics as labelled deductive systems. PhD thesis, Imperial College, London, 1996.

    Google Scholar 

  31. M. Tzakova. Tableau calculi for hybrid logics. In this volume, 1999.

    Google Scholar 

  32. L. Wallen. Automated Deduction in Nonclassical Logics. MIT Press, 1990.

    Google Scholar 

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Authors and Affiliations

  1. Laboratoire LEIBNIZ- U.M.R. 5522, 46 Avenue Felix Viallet, 38031, Grenoble, France

    Stéphane Demri

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  1. Stéphane Demri
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Editors and Affiliations

  1. Department of Computer Science, Institute for Programming and Logics, University at Albany - SUNY, Albany, NY, 12222, USA

    Neil V. Murray

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Demri, S. (1999). Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?. In: Murray, N.V. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1999. Lecture Notes in Computer Science(), vol 1617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48754-9_15

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  • DOI: https://doi.org/10.1007/3-540-48754-9_15

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  • Print ISBN: 978-3-540-66086-6

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