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International Conference on Automated Deduction

CADE 2009: Automated Deduction – CADE-22 pp 245–260Cite as

A Refined Resolution Calculus for CTL

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5663))

Abstract

In this paper, we present a refined resolution-based calculus for Computation Tree Logic (CTL). The calculus requires a polynomial time computable transformation of an arbitrary CTL formula to an equi-satisfiable clausal normal form formulated in an extension of CTL with indexed existential path quantifiers. The calculus itself consists of a set of resolution rules which can be used as the basis for an EXPTIME decision procedure for the satisfiability problem of CTL. We prove soundness and completeness of the calculus. In addition, we introduce CTL-RP, our implementation of the calculus as well as some experimental results.

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References

  1. Abate, P., Goré, R.: The Tableaux Workbench. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003. LNCS, vol. 2796, pp. 230–236. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Abate, P., Goré, R., Widmann, F.: One-Pass Tableaux for Computation Tree Logic. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS, vol. 4790, pp. 32–46. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Handbook of Automated Reasoning, vol. 1, pp. 19–99. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  5. Bolotov, A.: Clausal Resolution for Branching-Time Temporal Logic. PhD thesis, Manchester Metropolitan University (2000)

    Google Scholar 

  6. Bolotov, A., Dixon, C.: Resolution for Branching Time Temporal Logics: Applying the Temporal Resolution Rule. In: Proc. TIME 2000, pp. 163–172. IEEE, Los Alamitos (2000)

    Google Scholar 

  7. Clarke, E.M., Emerson, E.A.: Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  8. Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2000)

    Google Scholar 

  9. Dixon, C.: Temporal Resolution Using a Breadth-First Search Algorithm. Annals of Mathematics and Artificial Intelligence 22(1-2), 87–115 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Emerson, E.A.: Temporal and Modal Logic. In: Handbook of Theoretical Computer Science, pp. 996–1072. Elsevier, Amsterdam (1990)

    Google Scholar 

  11. Emerson, E.A., Halpern, J.Y.: Decision Procedures and Expressiveness in the Temporal Logic of Branching Time. J. Comput. Syst. Sci. 30(1), 1–24 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fisher, M., Dixon, C., Peim, M.: Clausal Temporal Resolution. ACM Transactions on Computational Logic 2(1), 12–56 (2001)

    Article  MathSciNet  Google Scholar 

  13. Hustadt, U., Konev, B.: TRP++: A Temporal Resolution Prover. In: Collegium Logicum, pp. 65–79. Kurt Gödel Society (2004)

    Google Scholar 

  14. Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning about Systems. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  15. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems. Springer, Heidelberg (1992)

    Book  MATH  Google Scholar 

  16. Max-Planck-Institut Informatik: SPASS: An Automated Theorem Prover for First- Order Logic with Equality, http://www.spass-prover.org/

  17. Vardi, M.Y., Wolper, P.: Automata-Theoretic Techniques for Modal Logics of Programs. J. Comput. Syst. Sci. 32(2), 183–221 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  18. Weidenbach, C., Schmidt, R.A., Hillenbrand, T., Rusev, R., Topic, D.: System description: Spass version 3.0. In: Pfenning, F. (ed.) CADE 2007. LNCS, vol. 4603, pp. 514–520. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Zhang, L., Hustadt, U., Dixon, C.: First-order Resolution for CTL. Technical Report ULCS-08-010, Department of Computer Science, University of Liverpool (2008)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK

    Lan Zhang, Ullrich Hustadt & Clare Dixon

Authors
  1. Lan Zhang
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  2. Ullrich Hustadt
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  3. Clare Dixon
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Editor information

Editors and Affiliations

  1. School of Computer Science, The University of Manchester, Manchester, UK

    Renate A. Schmidt

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Zhang, L., Hustadt, U., Dixon, C. (2009). A Refined Resolution Calculus for CTL. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-02959-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02958-5

  • Online ISBN: 978-3-642-02959-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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