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Solving the Entailment Problem in the Fluent Calculus Using Binary Decision Diagrams

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Computational Logic — CL 2000 (CL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1861))

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Abstract

It is rigorously shown how planning problems encoded as a class of entailment problems in the fluent calculus can be mapped onto satisfiability problems for propositional formulas, which in turn can be mapped to the problem of finding models using binary decision diagrams (BDDs). The mapping is shown to be sound and complete. First experimental results of an implementation are presented and discussed.

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References

  1. Avrim Blum and Merrick Furst. Fast planning through planning graph analysis. Artificial Intelligence, 90:281–300, 1997.

    Article  MATH  Google Scholar 

  2. Randal E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers, 8(C-35):677–691, 1986.

    Article  Google Scholar 

  3. J. Burch, E. Clarke, K. McMillan, and D. Dill. Symbolic model checking: 1020 states and beyond. Information and Computation, 98(2):142–170, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. R. Burch, E. M. Clarke, D. E. Long, K. L. McMillan, and D. L. Dill. Symbolic model checking for sequential circuit verification. IEEE Transactions on Computer-Aided Design of Integrated Circuits, 13(4):401–424, April 1994.

    Google Scholar 

  5. A. Cimatti, E. Giunchiglia, F. Giunchiglia, and P. Traverso. ”planning via model checking: A decision procedure for ar. In S. Steel and R. Alami, editors, Proceedings of the Fourth European Conference on Planning (ECP97), LNAI 1348, pages 130–142, Toulouse, France, Sept. 1997. Springer-Verlag.

    Google Scholar 

  6. Alessandro Cimatti, Marco Roveri, and Paolo Traverso. Automatic OBDD-based generation of universal plans on non-deterministic domains. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI98), Madison, Wisconsin, July 26–30 1998.

    Google Scholar 

  7. E. Clarke, O. Grunberg, and D. Long. Model checking. In Proceedings of the International Summer School on Deductive Program Design, Marktoberdorf, 1994.

    Google Scholar 

  8. Stefan Edelkamp and Malte Helmert. Exhibiting knowledge in planning problems to minimize state encoding length. In ECP’99, LNAI, pages 135–147, Durham, 1999. Springer.

    Google Scholar 

  9. T. Eiter, N. Leone, C. Mateis, G. Pfeier, and F. Scarnello. The KR system DLV: Progress report, comparisons and benchmarks. In Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning, pages 406–417. Morgan Kaufmann Publishers, 1998.

    Google Scholar 

  10. M. Ghallab, A. Howe, C. Knoblock, D. McDermott, A. Ram, M. Veloso, D. Weld, and D. Wilkins. The planning domain definition language. ftp://ftp.cs.yale.edu/pub/mcdermott/software/pddl.tar.gz, march 1998.

  11. S. Hölldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225–244, 1990.

    Article  MATH  Google Scholar 

  12. S. Hölldobler and H.-P. Störr. Solving the entailment problem in the fluent calculus using binary decision diagrams. Technical Report WV-99-05, AI-Institute, Computer Science Department, Dresden University of Technology, 1999.

    Google Scholar 

  13. Henry Kautz and Bart Selman. Pushing the envelope: Planning, propositional logic, and stochastic search. In Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI-96), pages 1194–1201, Portland, Oregon, 1996. AAAI-Press.

    Google Scholar 

  14. J. McCarthy. Situations and actions and causal laws. Stanford Artificial Intelligence Project: Memo 2, 1963.

    Google Scholar 

  15. Drew McDermott. Planning problem repository. ftp://ftp.cs.yale.edu/pub/mcdermott/domains/, 1999.

  16. I. Niemelä and P. Simons. Smodels — an implementation of the well-founded and stable model semantics. In Proceedings of the 4th International Conderence on Logic Programming and Non-monotonic Reasoning, pages 420–429, 1997.

    Google Scholar 

  17. B. Selman, H. Levesque, and D. Mitchell. A new method for solving hard satisfiability problems. In Proceedings of the AAAI National Conference on Artificial Intelligence, pages 440–446, 1992.

    Google Scholar 

  18. H.-P. Störr. Planen mit binären Entscheidungsdiagrammen. PhD thesis, Dresden University of Technology, Department of Computer Science, 2000. (in German; to appear).

    Google Scholar 

  19. H.-P. Störr and M. Thielscher. A new equational foundation for the fluent calculus. In Proceedings CL 2000.

    Google Scholar 

  20. Michael Thielscher. Introduction to the Fluent Calculus. Electronic Transactions on Artificial Intelligence, 2(3–4):179–192, 1998.

    MathSciNet  Google Scholar 

  21. Michael Thielscher. Reasoning about actions: Steady versus stabilizing state constraints. Artificial Intelligence, 104:339–355, 1998.

    Article  MATH  MathSciNet  Google Scholar 

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Hölldobler, S., Störr, HP. (2000). Solving the Entailment Problem in the Fluent Calculus Using Binary Decision Diagrams. In: Lloyd, J., et al. Computational Logic — CL 2000. CL 2000. Lecture Notes in Computer Science(), vol 1861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44957-4_50

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  • DOI: https://doi.org/10.1007/3-540-44957-4_50

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  • Print ISBN: 978-3-540-67797-0

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