Advertisement

Decidable Verification of Decision-Theoretic Golog

  • Jens ClaßenEmail author
  • Benjamin Zarrieß
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10483)

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.

Notes

Acknowledgments

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

References

  1. 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 CrossRefGoogle Scholar
  2. 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. 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. 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 CrossRefGoogle Scholar
  5. 5.
    Ferrein, A., Lakemeyer, G.: Logic-based robot control in highly dynamic domains. Robot. Auton. Syst. 56, 980–991 (2008)CrossRefGoogle Scholar
  6. 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 CrossRefGoogle Scholar
  7. 7.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Aspects Comput. 6(5), 512–535 (1994)CrossRefzbMATHGoogle Scholar
  8. 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 zbMATHGoogle Scholar
  9. 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. 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 CrossRefGoogle Scholar
  11. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lin, F., Reiter, R.: How to progress a database. Artif. Intell. 92(1–2), 131–167 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Pednault, E.P.D.: Synthesizing plans that contain actions with context-dependent effects. Comput. Intell. 4, 356–372 (1988)CrossRefGoogle Scholar
  15. 15.
    Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)CrossRefzbMATHGoogle Scholar
  16. 16.
    Reiter, R.: Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  17. 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. 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. 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. 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

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Knowledge-Based Systems GroupRWTH Aachen UniversityAachenGermany
  2. 2.Theoretical Computer ScienceTU DresdenDresdenGermany

Personalised recommendations