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Satisfiability and Completeness of Converse-PDL Replayed

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KI 2003: Advances in Artificial Intelligence (KI 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2821))

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Abstract

This paper reinvestigates the satisfiability problem and the issue of completeness for Propositional Dynamic Logic with Converse. By giving a game-theoretic characterisation of its satisfiability problem using focus games, an axiom system that is extracted from these games can easily be proved to be complete.

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References

  1. Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. Journal of the ACM 28(1), 114–133 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  2. Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18(2), 194–211 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  3. de Giacomo, G., Massacci, F.: Combining deduction and model checking into tableaux and algorithms for Converse-PDL. Information and Computation 162, 117–137 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kozen, D.: Results on the propositional μ-calculus. TCS 27, 333–354 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kozen, D., Parikh, R.: An elementary proof of the completeness of PDL (note). TCS 14, 113–118 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lange, M., Stirling, C.: Model checking games for CTL∗. In: Proc. Conf. on Temporal Logic, ICTL 2000, Leipzig, Germany, pp. 115–125 (2000)

    Google Scholar 

  7. Lange, M., Stirling, C.: Focus games for satisfiability and completeness of temporal logic. In: Proc. 16th Symp. on Logic in Computer Science, LICS 2001, Boston, MA, USA, IEEE, Los Alamitos (2001)

    Google Scholar 

  8. Pratt, V.R.: A practical decision method for propositional dynamic logic. In: Proc. 10th Symp. on Theory of Computing, STOC 1978, San Diego, California, pp. 326–337 (May 1978)

    Google Scholar 

  9. Pratt, V.R.: Models of program logics. In: Proc. 20th Symp. on Foundations of Computer Science, FOCS 1979, pp. 115–122. IEEE, Los Alamitos (1979)

    Chapter  Google Scholar 

  10. Segerberg, K.: A completeness theorem in the modal logic of programs. Notices of the AMS 24(6), A–552 (1977)

    Google Scholar 

  11. Stirling, C.: Modal and temporal logics. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Background: Computational Structures. Handbook of Logic in Computer Science, vol. 2, pp. 477–563. Clarendon Press, Oxford (1992)

    Google Scholar 

  12. Streett, R.S.: Propositional dynamic logic of looping and converse is elementarily decidable. Information and Control 54(1/2), 121–141 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  13. Vardi, M.Y., Wolper, P.: Automata-theoretic techniques for modal logic of programs. Journal of Computer and System Sciences 32, 183–221 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  14. Woods, W.A., Schmolze, J.G.: The kl-one family. In: Lehmann, F. (ed.) Semantic Networks in Artificial Intelligence, pp. 133–177. Pergamon Press, Oxford (1992)

    Google Scholar 

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Lange, M. (2003). Satisfiability and Completeness of Converse-PDL Replayed. In: Günter, A., Kruse, R., Neumann, B. (eds) KI 2003: Advances in Artificial Intelligence. KI 2003. Lecture Notes in Computer Science(), vol 2821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39451-8_7

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  • DOI: https://doi.org/10.1007/978-3-540-39451-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20059-8

  • Online ISBN: 978-3-540-39451-8

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