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Decidable Verification of Decision-Theoretic Golog

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Frontiers of Combining Systems (FroCoS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10483))

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Abstract

The Golog agent programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. Its variant DTGolog includes decision-theoretic aspects in the form of stochastic (probabilistic) actions and reward functions. In particular for physical systems such as robots, verifying that a program satisfies certain desired temporal properties is often crucial, but undecidable in general, the latter being due to the language’s high expressiveness in terms of first-order quantification, range of action effects, and program constructs. Recent results for classical Golog show that by suitably restricting these aspects, the verification problem becomes decidable for a non-trivial fragment that retains a large degree of expressiveness. In this paper, we lift these results to the decision-theoretic case by providing an abstraction mechanism for reducing the infinite-state Markov Decision Process induced by the DTGolog program to a finite-state representation, which then can be fed into a state-of-the-art probabilistic model checker.

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Notes

  1. 1.

    Note that we can always simulate a deterministic action by a stochastic one that has only one outcome.

References

  1. Andova, S., Hermanns, H., Katoen, J.-P.: Discrete-time rewards model-checked. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 88–104. Springer, Heidelberg (2004). doi:10.1007/978-3-540-40903-8_8

    Chapter  Google Scholar 

  2. Boutilier, C., Reiter, R., Soutchanski, M., Thrun, S.: Decision-theoretic, high-level agent programming in the situation calculus. In: Kautz, H., Porter, B. (eds.) Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI 2000), pp. 355–362. AAAI Press (2000)

    Google Scholar 

  3. Claßen, J., Lakemeyer, G.: A logic for non-terminating Golog programs. In: Brewka, G., Lang, J. (eds.) Proceedings of the Eleventh International Conference on the Principles of Knowledge Representation and Reasoning (KR 2008), pp. 589–599. AAAI Press (2008)

    Google Scholar 

  4. Dehnert, C., Junges, S., Katoen, J.P., Volk, M.: A storm is coming: a modern probabilistic model checker. In: Kuncak, V., Majumdar, R. (eds.) CAV 2017. Theoretical Computer Science and General Issues, vol. 10427, pp. 592–600. Springer, Heidelberg (2017). doi:10.1007/978-3-319-63390-9_31

    Chapter  Google Scholar 

  5. Ferrein, A., Lakemeyer, G.: Logic-based robot control in highly dynamic domains. Robot. Auton. Syst. 56, 980–991 (2008)

    Article  Google Scholar 

  6. Forejt, V., Kwiatkowska, M., Norman, G., Parker, D.: Automated verification techniques for probabilistic systems. In: Bernardo, M., Issarny, V. (eds.) SFM 2011. LNCS, vol. 6659, pp. 53–113. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21455-4_3

    Chapter  Google Scholar 

  7. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Aspects Comput. 6(5), 512–535 (1994)

    Article  MATH  Google Scholar 

  8. Kemeny, J.G., Snell, J.L., Knapp, A.W.: Denumerable Markov Chains. Graduate Texts in Mathematics, vol. 40. Springer, New York (1976). doi:10.1007/978-1-4684-9455-6

    MATH  Google Scholar 

  9. Kwiatkowska, M., Parker, D.: Advances in probabilistic model checking. In: Nipkow, T., Grumberg, O., Hauptmann, B. (eds.) Software Safety and Security - Tools for Analysis and Verification, NATO Science for Peace and Security Series - D: Information and Communication Security, vol. 33, pp. 126–151. IOS Press (2012)

    Google Scholar 

  10. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22110-1_47

    Chapter  Google Scholar 

  11. Lakemeyer, G., Levesque, H.J.: A semantic characterization of a useful fragment of the situation calculus with knowledge. Artif. Intell. 175(1), 142–164 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Levesque, H.J., Reiter, R., Lespérance, Y., Lin, F., Scherl, R.B.: GOLOG: a logic programming language for dynamic domains. J. Log. Program. 31(1–3), 59–83 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lin, F., Reiter, R.: How to progress a database. Artif. Intell. 92(1–2), 131–167 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pednault, E.P.D.: Synthesizing plans that contain actions with context-dependent effects. Comput. Intell. 4, 356–372 (1988)

    Article  Google Scholar 

  15. Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)

    Book  MATH  Google Scholar 

  16. Reiter, R.: Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  17. Soutchanski, M.: An on-line decision-theoretic Golog interpreter. In: Nebel, B. (ed.) Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence (IJCAI 2001), pp. 19–26. Morgan Kaufmann Publishers Inc. (2001)

    Google Scholar 

  18. Vassos, S., Lakemeyer, G., Levesque, H.J.: First-order strong progression for local-effect basic action theories. In: Brewka, G., Lang, J. (eds.) Proceedings of the Eleventh International Conference on the Principles of Knowledge Representation and Reasoning (KR 2008), pp. 662–672. AAAI Press (2008)

    Google Scholar 

  19. Zarrieß, B., Claßen, J.: Decidable verification of Golog programs over non-local effect actions. LTCS-Report 15-19, Chair of Automata Theory, TU Dresden, Dresden, Germany (2015)

    Google Scholar 

  20. Zarrieß, B., Claßen, J.: Decidable verification of Golog programs over non-local effect actions. In: Schuurmans, D., Wellman, M. (eds.) Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI 2016), pp. 1109–1115. AAAI Press (2016)

    Google Scholar 

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Acknowledgments

This work was supported by the German Research Foundation (DFG) research unit FOR 1513 on Hybrid Reasoning for Intelligent Systems, project A1.

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Authors and Affiliations

  1. Knowledge-Based Systems Group, RWTH Aachen University, Aachen, Germany

    Jens Claßen

  2. Theoretical Computer Science, TU Dresden, Dresden, Germany

    Benjamin Zarrieß

Authors
  1. Jens Claßen
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  2. Benjamin Zarrieß
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Correspondence to Jens Claßen .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Clare Dixon

  2. University of Sao Paulo, Sao Paulo, Brazil

    Marcelo Finger

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Claßen, J., Zarrieß, B. (2017). Decidable Verification of Decision-Theoretic Golog . In: Dixon, C., Finger, M. (eds) Frontiers of Combining Systems. FroCoS 2017. Lecture Notes in Computer Science(), vol 10483. Springer, Cham. https://doi.org/10.1007/978-3-319-66167-4_13

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  • DOI: https://doi.org/10.1007/978-3-319-66167-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66166-7

  • Online ISBN: 978-3-319-66167-4

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