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