Advertisement

Situation Calculus Meets Description Logics

  • Jens ClaßenEmail author
  • Gerhard Lakemeyer
  • Benjamin Zarrieß
Chapter
First Online:
  • 433 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11560)

Abstract

For more than six years, the groups of Franz Baader and Gerhard Lakemeyer have collaborated in the area of decidable verification of Golog programs. Golog is an action programming language, whose semantics is based on the Situation Calculus, a variant of full first-order logic. In order to achieve decidability, the expressiveness of the base logic had to be restricted, and using a Description Logic was a natural choice. In this chapter, we highlight some of the main results and insights obtained during our collaboration.

Keywords

Situation Calculus Description Logics Verification 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

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).  https://doi.org/10.1007/978-3-540-40903-8_8CrossRefGoogle Scholar
  2. 2.
    Baader, F., Ghilardi, S., Lutz, C.: LTL over description logic axioms. In: Proceedings of the Eleventh International Conference on the Principles of Knowledge Representation and Reasoning (KR 2008), pp. 684–694. AAAI Press (2008)Google Scholar
  3. 3.
    Baader, F., Lippmann, M., Liu, H.: Using causal relationships to deal with the ramification problem in action formalisms based on description logics. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR 2010. LNCS, vol. 6397, pp. 82–96. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-16242-8_7CrossRefGoogle Scholar
  4. 4.
    Baader, F., Liu, H., ul Mehdi, A.: Verifying properties of infinite sequences of description logic actions. In: Proceedings of the Nineteenth European Conference on Artificial Intelligence (ECAI 2010). Frontiers in Artificial Intelligence and Applications, vol. 215, pp. 53–58. IOS Press (2010)Google Scholar
  5. 5.
    Baader, F., Lutz, C., Miličić, M., Sattler, U., Wolter, F.: Integrating description logics and action formalisms: first results. In: Proceedings of the Twentieth National Conference on Artificial Intelligence (AAAI 2005), pp. 572–577. AAAI Press (2005)Google Scholar
  6. 6.
    Baader, F., Zarrieß, B.: Verification of Golog programs over description logic actions. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS (LNAI), vol. 8152, pp. 181–196. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40885-4_12CrossRefzbMATHGoogle Scholar
  7. 7.
    Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  8. 8.
    Boutilier, C., Reiter, R., Soutchanski, M., Thrun, S.: Decision-theoretic, high-level agent programming in the situation calculus. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI 2000). pp. 355–362. AAAI Press (2000)Google Scholar
  9. 9.
    Brewka, G., Lakemeyer, G.: Hybrid reasoning for intelligent systems: a focus of KR research in Germany. AI Mag. 39(4), 80–83 (2018)CrossRefGoogle Scholar
  10. 10.
    Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)CrossRefGoogle Scholar
  11. 11.
    Burgard, W., et al.: Experiences with an interactive museum tour-guide robot. Artif. Intell. 114(1–2), 3–55 (1999)CrossRefGoogle Scholar
  12. 12.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  13. 13.
    Claßen, J.: Planning and verification in the agent language Golog. Ph.D. thesis, Department of Computer Science, RWTH Aachen University (2013). http://darwin.bth.rwth-aachen.de/opus3/volltexte/2013/4809/
  14. 14.
    Claßen, J.: Symbolic verification of Golog programs with first-order BDDs. In: Proceedings of the Sixteenth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2018), pp. 524–529. AAAI Press (2018)Google Scholar
  15. 15.
    Claßen, J., Lakemeyer, G.: Foundations for knowledge-based programs using \(\cal{E\!S}\). In: Proceedings of the Tenth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2006), pp. 318–328. AAAI Press (2006)Google Scholar
  16. 16.
    Claßen, J., Lakemeyer, G.: A logic for non-terminating Golog programs. In: Proceedings of the Eleventh International Conference on the Principles of Knowledge Representation and Reasoning (KR 2008), pp. 589–599. AAAI Press (2008)Google Scholar
  17. 17.
    Claßen, J., Liebenberg, M., Lakemeyer, G., Zarrieß, B.: Exploring the boundaries of decidable verification of non-terminating Golog programs. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence (AAAI 2014), pp. 1012–1019. AAAI Press (2014)Google Scholar
  18. 18.
    Claßen, J., Zarrieß, B.: Decidable verification of decision-theoretic Golog. In: Dixon, C., Finger, M. (eds.) FroCoS 2017. LNCS (LNAI), vol. 10483, pp. 227–243. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66167-4_13CrossRefzbMATHGoogle Scholar
  19. 19.
    De Giacomo, G., Lespérance, Y., Levesque, H.J.: ConGolog, a concurrent programming language based on the situation calculus. Artif. Intell. 121(1–2), 109–169 (2000)MathSciNetCrossRefGoogle Scholar
  20. 20.
    De Giacomo, G., Lespérance, Y., Patrizi, F., Sardiña, S.: Verifying ConGolog programs on bounded situation calculus theories. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI 2016), pp. 950–956. AAAI Press (2016)Google Scholar
  21. 21.
    De Giacomo, G., Ternovska, E., Reiter, R.: Non-terminating processes in the situation calculus. In: Working Notes of “Robots, Softbots, Immobots: Theories of Action, Planning and Control”, AAAI 1997 Workshop (1997)Google Scholar
  22. 22.
    Dehnert, C., Junges, S., Katoen, J.-P., Volk, M.: A Storm is coming: a modern probabilistic model checker. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 592–600. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63390-9_31CrossRefGoogle Scholar
  23. 23.
    Donini, F.M., Lenzerini, M., Nardi, D., Nutt, W., Schaerf, A.: An epistemic operator for description logics. Artif. Intell. 100(1–2), 225–274 (1998)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Ferrein, A., Niemueller, T., Schiffer, S., Lakemeyer, G.: Lessons learnt from developing the embodied AI platform CAESAR for domestic service robotics. In: Papers from the AAAI 2013 Spring Symposium on Designing Intelligent Robots: Reintegrating AI II. Technical report SS-13-04, AAAI Press (2013)Google Scholar
  25. 25.
    Grädel, E., Kolaitis, P.G., Vardi, M.Y.: On the decision problem for two-variable first-order logic. Bull. Symb. Log. 3(1), 53–69 (1997)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Gu, Y., Soutchanski, M.: A description logic based situation calculus. Ann. Math. Artif. Intell. 58(1–2), 3–83 (2010)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Halpern, J.Y.: An analysis of first-order logics of probability. Artif. Intell. 46(3), 311–350 (1990).  https://doi.org/10.1016/0004-3702(90)90019-VMathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Asp. Comput. 6(5), 512–535 (1994)CrossRefGoogle Scholar
  29. 29.
    Koopmann, P., Zarrieß, B.: On the complexity of verifying timed Golog programs over description logic actions. In: Proceedings of the 2018 Workshop on Hybrid Reasoning and Learning (HRL 2018) (2018)Google Scholar
  30. 30.
    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).  https://doi.org/10.1007/978-3-642-22110-1_47CrossRefGoogle Scholar
  31. 31.
    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)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Laroussinie, F., Markey, N., Schnoebelen, P.: Efficient timed model checking for discrete-time systems. Theor. Comput. Sci. 353(1–3), 249–271 (2006).  https://doi.org/10.1016/j.tcs.2005.11.020MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    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)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Li, N., Liu, Y.: Automatic verification of partial correctness of Golog programs. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI 2015), pp. 3113–3119. AAAI Press (2015)Google Scholar
  35. 35.
    Lin, F., Reiter, R.: How to progress a database. Artif. Intell. 92(1–2), 131–167 (1997)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Liu, H., Lutz, C., Miličić, M., Wolter, F.: Reasoning about actions using description logics with general TBoxes. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 266–279. Springer, Heidelberg (2006).  https://doi.org/10.1007/11853886_23CrossRefzbMATHGoogle Scholar
  37. 37.
    Liu, Y., Lakemeyer, G.: On first-order definability and computability of progression for local-effect actions and beyond. In: Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence (IJCAI 2009), pp. 860–866. AAAI Press (2009)Google Scholar
  38. 38.
    Liu, Y., Levesque, H.J.: Tractable reasoning with incomplete first-order knowledge in dynamic systems with context-dependent actions. In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 522–527. Professional Book Center (2005)Google Scholar
  39. 39.
    Lutz, C., Schröder, L.: Probabilistic description logics for subjective uncertainty. In: Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2010). AAAI Press (2010)Google Scholar
  40. 40.
    McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 4, pp. 463–502. American Elsevier, New York (1969)zbMATHGoogle Scholar
  41. 41.
    McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Norwell (1993)CrossRefGoogle Scholar
  42. 42.
    Pednault, E.P.D.: Synthesizing plans that contain actions with context-dependent effects. Comput. Intell. 4, 356–372 (1988)CrossRefGoogle Scholar
  43. 43.
    Reiter, R.: The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression. Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy pp. 359–380 (1991)CrossRefGoogle Scholar
  44. 44.
    Reiter, R.: Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. MIT Press, Cambridge (2001)CrossRefGoogle Scholar
  45. 45.
    Reiter, R.: On knowledge-based programming with sensing in the situation calculus. ACM Trans. Comput. Log. 2(4), 433–457 (2001)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Sanner, S., Boutilier, C.: Practical solution techniques for first-order MDPs. Artif. Intell. 173(5–6), 748–788 (2009)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Schulz, S.: System description: E 1.8. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR 2013. LNCS, vol. 8312, pp. 735–743. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-45221-5_49CrossRefGoogle Scholar
  48. 48.
    Soutchanski, M.: An on-line decision-theoretic Golog interpreter. In: Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence (IJCAI 2001), pp. 19–26. Morgan Kaufmann Publishers Inc. (2001)Google Scholar
  49. 49.
    Zarrieß, B.: Complexity of projection with stochastic actions in a probabilistic description logic. In: Proceedings of the Sixteenth International Conference on the Principles of Knowledge Representation and Reasoning (KR 2018), pp. 514–523. AAAI Press (2018)Google Scholar
  50. 50.
    Zarrieß, B.: Verification of Golog programs over description logic actions. Ph.D. thesis, Dresden University of Technology, Germany (2018). http://d-nb.info/116636531X
  51. 51.
    Zarrieß, B., Claßen, J.: On the decidability of verifying LTL properties of Golog programs. In: Proceedings of the AAAI 2014 Spring Symposium: Knowledge Representation and Reasoning in Robotics (KRR 2014). AAAI Press, Palo Alto (2014)Google Scholar
  52. 52.
    Zarrieß, B., Claßen, J.: Verifying CTL* properties of Golog programs over local-effect actions. In: Proceedings of the Twenty-First European Conference on Artificial Intelligence (ECAI 2014), pp. 939–944. IOS Press (2014)Google Scholar
  53. 53.
    Zarrieß, B., Claßen, J.: Decidable verification of knowledge-based programs over description logic actions with sensing. In: Proceedings of the Twenty-Eighth International Workshop on Description Logics (DL 2015). CEUR Workshop Proceedings, vol. 1350. CEUR-WS.org (2015)Google Scholar
  54. 54.
    Zarrieß, B., Claßen, J.: Verification of knowledge-based programs over description logic actions. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI 2015), pp. 3278–3284. AAAI Press (2015)Google Scholar
  55. 55.
    Zarrieß, B., Claßen, J.: Decidable verification of Golog programs over non-local effect actions. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI 2016), pp. 1109–1115. AAAI Press (2016)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jens Claßen
    • 1
    Email author
  • Gerhard Lakemeyer
    • 2
  • Benjamin Zarrieß
    • 3
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Knowledge-Based Systems GroupRWTH Aachen UniversityAachenGermany
  3. 3.Institute of Theoretical Computer ScienceTechnische Universität DresdenDresdenGermany

Personalised recommendations

Cite chapter

Buy options