Studia Logica

, Volume 104, Issue 4, pp 705–739 | Cite as

Progression and Verification of Situation Calculus Agents with Bounded Beliefs

  • Giuseppe De Giacomo
  • Yves Lespérance
  • Fabio Patrizi
  • Stavros Vassos
Open Access


We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories.


Reasoning about actions Situation calculus Progression Online execution Verification of agent behaviors Mu-Calculus 


  1. 1.
    Bagheri Hariri, B., D. Calvanese, G. De Giacomo, R. De Masellis, and P. Felli, Foundations of relational artifacts verification, in Proceedings of BPM, 2011.Google Scholar
  2. 2.
    Bagheri Hariri, B., D. Calvanese, G. De Giacomo, A. Deutsch, and M. Montali, Verification of relational data-centric dynamic systems with external services, in Proceedings of PODS, 2013.Google Scholar
  3. 3.
    Baier C., Katoen J.-P., Guldstrand Larsen K.: Principles of Model Checking. MIT Press, Cambridge (2008)Google Scholar
  4. 4.
    Belardinelli F., Lomuscio A., Patrizi F.: Verification of agent-based artifact systems. Journal of Artificial Intelligence Research 51, 333–376 (2014)Google Scholar
  5. 5.
    Bonet B.: Conformant plans and beyond: Principles and complexity. Artificial Intelligence Research 174(3–4), 245–269 (2010)CrossRefGoogle Scholar
  6. 6.
    Bordini, R. H., M. Fisher, C. Pardavila, and M. Wooldridge, Model checking agentspeak, in Proceedings of AAMAS, 2003.Google Scholar
  7. 7.
    Burkart, O., D. Caucal, F. Moller, and B. Steffen, Verification of infinite structures, in Handbook of Process Algebra, Elsevier Science, Amsterdam, 2001.Google Scholar
  8. 8.
    Classen, J., and G. Lakemeyer, A logic for non-terminating Golog programs, in Proceedings of KR, 2008.Google Scholar
  9. 9.
    Classen, J., M. Liebenberg, G. Lakemeyer, and B. Zarriess, Exploring the boundaries of decidable verification of non-terminating Golog programs, in Proceedings of AAAI, 2014.Google Scholar
  10. 10.
    De Giacomo, G., Y. Lespérance, H. J. Levesque, and S. Sardina, IndiGolog: A high-level programming language for embedded reasoning agents, in Multi-Agent Programming: Languages, Tools and Applications, Springer, Berlin, 2009.Google Scholar
  11. 11.
    De Giacomo, G., Y. Lespérance, and F. Patrizi, Bounded situation calculus action theories and decidable verification, in Proceedings of KR, 2012.Google Scholar
  12. 12.
    De Giacomo, G., Y. Lespérance, and F. Patrizi, Bounded epistemic situation calculus theories, in Proceedings of IJCAI, 2013.Google Scholar
  13. 13.
    De Giacomo, G., Y. Lespérance, F. Patrizi, and S. Vassos, LTL verification of online executions with sensing in bounded situation calculus, in Proceedings of ECAI, 2014.Google Scholar
  14. 14.
    De Giacomo, G., Y. Lespérance, F. Patrizi, and S. Vassos, Progression and verification of situation calculus agents with bounded beliefs, in Proceedings of AAMAS, 2014.Google Scholar
  15. 15.
    De Giacomo, G., Y. Lespérance, and A. R. Pearce, Situation calculus based programs for representing and reasoning about game structures, in Proceedings of KR, 2010.Google Scholar
  16. 16.
    De Giacomo G., and H. J. Levesque, An incremental interpreter for high-level programs with sensing, in Logical Foundations for Cognitive Agents: Contributions in Honor of Ray Reiter, Springer, Berlin, 1999.Google Scholar
  17. 17.
    De Giacomo, G., and H. J. Levesque, Projection using regression and sensors, in Proceedings of IJCAI, 1999.Google Scholar
  18. 18.
    Dennis L. A., Fisher M., Webster M. P., Bordini R. H.: Model checking agent programming languages. Automated Software Engineering 19(1), 5–63 (2012)CrossRefGoogle Scholar
  19. 19.
    Deutsch, A., R. Hull, F. Patrizi, and V. Vianu, Automatic verification of data-centric business processes, in Proceedings of ICDT, 2009.Google Scholar
  20. 20.
    Dumas, M., W. M. P. van der Aalst, and A. H. M. ter Hofstede, Process-Aware Information Systems: Bridging People and Software Through Process Technology. Wiley, Hoboken, 2005.Google Scholar
  21. 21.
    Emerson, E. A., Model checking and the Mu-calculus, in Descriptive Complexity and Finite Models. Proceedings of a DIMACS Workshop, 1996.Google Scholar
  22. 22.
    Gerede, C. E., and J. Su, Specification and verification of artifact behaviors in business process models, in Proceedings of ICSOC, 2007.Google Scholar
  23. 23.
    Gu, Y., and M. Soutchanski, Decidable reasoning in a modified situation calculus, in Proceedings of IJCAI 2007.Google Scholar
  24. 24.
    Hull, R., Artifact-centric business process models: Brief survey of research results and challenges, in Proceedings of OTM 2008 Confederated International Conferences, 2008.Google Scholar
  25. 25.
    Lakemeyer, G., and H. J. Levesque, Situations, si! situation terms, no!, in Proceedings of KR, 2004.Google Scholar
  26. 26.
    Lakemeyer, G., and H. J. Levesque, Semantics for a useful fragment of the situation calculus, in Proceedings of IJCAI, 2005.Google Scholar
  27. 27.
    Levesque H. J., Reiter R., Lespérance Y., Lin F., Scherl R. B.: GOLOG: A Logic Programming Language for Dynamic Domains. Journal of Logic Programming 31, 59–84 (1997)CrossRefGoogle Scholar
  28. 28.
    Libkin, L., Embedded finite models and constraint databases, in Finite Model Theory and Its Applications, Springer, Heidelberg, 2007.Google Scholar
  29. 29.
    Lin F., Reiter R.: How to progress a database. Artificial Intelligence 92(1–2), 131–167 (1997)CrossRefGoogle Scholar
  30. 30.
    Liu, Y., and G. Lakemeyer, On first-order definability and computability of progression for local-effect actions and beyond, in Proceedings of IJCAI, 2009.Google Scholar
  31. 31.
    Liu, Y., and H. J. Levesque, Tractable reasoning with incomplete first-order knowledge in dynamic systems with context-dependent actions, in Proceedings of IJCAI, 2005.Google Scholar
  32. 32.
    Lomuscio, A., H. Qu, and F. Raimondi, MCMAS: A model checker for the verification of multi-agent systems, in Proceedings of CAV, 2009.Google Scholar
  33. 33.
    McCarthy J., Hayes P. J.: Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence 4, 463–502 (1969)Google Scholar
  34. 34.
    Moore, R. C., A formal theory of knowledge and action, in J. R. Hobbs and R. C. Moore (eds.), Formal Theories of the Common Sense World, Ablex Publishing, Norwood, NJ, 1985, pp. 319–358.Google Scholar
  35. 35.
    Pirri F., Reiter R.: Some contributions to the metatheory of the situation calculus. Journal of ACM 46(3), 261–325 (1999)CrossRefGoogle Scholar
  36. 36.
    Reiter, R., Knowledge in Action. Logical Foundations for Specifying and Implementing Dynamical Systems, MIT Press, Cambridge, 2001.Google Scholar
  37. 37.
    Sardina, S., and G. De Giacomo, Composition of ConGolog programs, in Proceedings of IJCAI, 2009.Google Scholar
  38. 38.
    Sardina, S., G. De Giacomo, Y. Lespérance, and H. J. Levesque, On the semantics of deliberation in IndiGolog—from theory to implementation. Annals of Mathematics and Artificial Intelligence 41(2–4):259–299, 2004.Google Scholar
  39. 39.
    Sardina, S., G. D. Giacomo, Y. Lespérance, and H. J. Levesque, On ability to autonomously execute agent programs with sensing, in Proceedings of AAMAS, 2004.Google Scholar
  40. 40.
    Sardina, S., G. D. Giacomo, Y. Lespérance, and H. J. Levesque, On the limits of planning over belief states under strict uncertainty, in Proceedings of KR, 2006.Google Scholar
  41. 41.
    Scherl, R. B., and H. J. Levesque, The frame problem and knowledge-producing actions, in Proceedings of AAAI, 1993.Google Scholar
  42. 42.
    Scherl R. B., Levesque H. J.: Knowledge, action, and the frame problem. Artificial Intelligence 144(1–2), 1–39 (2003)CrossRefGoogle Scholar
  43. 43.
    Shapiro, S., Y. Lespérance, and H. J. Levesque, The cognitive agents specification language and verification environment for multiagent systems, in Proceedings of AAMAS, 2002.Google Scholar
  44. 44.
    Shapiro, S., Y. Lespérance, and H. J. Levesque, The cognitive agent specification language and verification environment, in M. Dastani, K. Hindriks, and J.-J. C. Meyer (eds.), Specification and Verification of Multi-agent Systems/Programs, Springer, Berlin, 2010, pp. 289–316.Google Scholar
  45. 45.
    Stirling, C., Modal and Temporal Properties of Processes, Springer, Heidelberg, 2001.Google Scholar
  46. 46.
    Ternovskaia, E., Automata theory for reasoning about actions, In Proceedings of IJCAI, 1999.Google Scholar
  47. 47.
    van Riemsdijk, M., L. Atefnoaei, and F. de Boer, Using the Maude term rewriting language for agent development with formal foundations, in M. Dastani, K. V. Hindriks, and J.-J. C. Meyer (eds.), Specification and Verification of Multi-agent Systems. Springer, Berlin, 2010, pp. 255–287.Google Scholar
  48. 48.
    Vardi, M. Y., An automata-theoretic approach to linear temporal logic, in Proceedings of Banff Higher Order Workshop, 1995.Google Scholar
  49. 49.
    Vassos, S., G. Lakemeyer, and H. J. Levesque, First-order strong progression for local-effect basic action theories, in Proceedings of KR, 2008.Google Scholar
  50. 50.
    Vassos, S., and H. J. Levesque, How to progress a database III, Artificial Intelligence 195:203–221, 2013.Google Scholar
  51. 51.
    Vassos, S., and F. Patrizi, A classification of first-order progressable action theories in situation calculus, in In Proceedings of IJCAI, 2013.Google Scholar
  52. 52.
    Wooldridge, M., Lomuscio A.:A computationally grounded logic of visibility, perception, and knowledge. Logic Journal of the IGPL 9(2):257–272 (2001)Google Scholar
  53. 53.
    Yadav, N., and S. Sardina, Reasoning about BDI agent programs using ATL-like logics, in Proceedings of JELIA, 2012.Google Scholar

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© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Giuseppe De Giacomo
    • 1
  • Yves Lespérance
    • 2
  • Fabio Patrizi
    • 3
  • Stavros Vassos
    • 1
  1. 1.Sapienza University of RomeRomeItaly
  2. 2.York UniversityTorontoCanada
  3. 3.Free University of Bozen-BolzanoBozen-BolzanoItaly

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