[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
Springer Nature Link
Log in

Situation Calculus Meets Description Logics

  • Chapter
  • First Online:
Description Logic, Theory Combination, and All That

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11560))

  • 776 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 35.99
Price includes VAT (United Kingdom)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 44.99
Price includes VAT (United Kingdom)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Free variables are understood as universally quantified from the outside; \(\Box \) has lower syntactic precedence than the logical connectives, [t] has higher precedence than the logical connectives. So \(\Box [a]F(\mathbf {x}) \equiv \gamma _F\) abbreviates \(\forall a,\mathbf {x}.\Box (([a]F(\mathbf {x})) \equiv \gamma _F)\).

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). https://doi.org/10.1007/978-3-540-40903-8_8

    Chapter  Google Scholar 

  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. 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_7

    Chapter  Google Scholar 

  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. 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. 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_12

    Chapter  MATH  Google Scholar 

  7. Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  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. Brewka, G., Lakemeyer, G.: Hybrid reasoning for intelligent systems: a focus of KR research in Germany. AI Mag. 39(4), 80–83 (2018)

    Article  Google Scholar 

  10. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)

    Article  Google Scholar 

  11. Burgard, W., et al.: Experiences with an interactive museum tour-guide robot. Artif. Intell. 114(1–2), 3–55 (1999)

    Article  Google Scholar 

  12. Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)

    Google Scholar 

  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. 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. 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. 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. 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. 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_13

    Chapter  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. 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. 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_31

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  26. Gu, Y., Soutchanski, M.: A description logic based situation calculus. Ann. Math. Artif. Intell. 58(1–2), 3–83 (2010)

    Article  MathSciNet  Google Scholar 

  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-V

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  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. 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_47

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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.2005.11.020

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  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_23

    Chapter  MATH  Google Scholar 

  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. 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. 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. 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)

    MATH  Google Scholar 

  41. McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Norwell (1993)

    Book  Google Scholar 

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

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

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

    Book  Google Scholar 

  45. Reiter, R.: On knowledge-based programming with sensing in the situation calculus. ACM Trans. Comput. Log. 2(4), 433–457 (2001)

    Article  MathSciNet  Google Scholar 

  46. Sanner, S., Boutilier, C.: Practical solution techniques for first-order MDPs. Artif. Intell. 173(5–6), 748–788 (2009)

    Article  MathSciNet  Google Scholar 

  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_49

    Chapter  Google Scholar 

  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. 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. 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. 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. 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. 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. 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. 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 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. School of Computing Science, Simon Fraser University, Burnaby, Canada

    Jens Claßen

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

    Gerhard Lakemeyer

  3. Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany

    Benjamin Zarrieß

Authors
  1. Jens Claßen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerhard Lakemeyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Benjamin Zarrieß
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jens Claßen .

Editor information

Editors and Affiliations

  1. University of Bremen, Bremen, Germany

    Carsten Lutz

  2. University of Manchester, Manchester, UK

    Uli Sattler

  3. University of Iowa, Iowa City, IA, USA

    Cesare Tinelli

  4. TU Dresden, Dresden, Germany

    Anni-Yasmin Turhan

  5. University of Liverpool, Liverpool, UK

    Frank Wolter

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Claßen, J., Lakemeyer, G., Zarrieß, B. (2019). Situation Calculus Meets Description Logics. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, AY., Wolter, F. (eds) Description Logic, Theory Combination, and All That. Lecture Notes in Computer Science(), vol 11560. Springer, Cham. https://doi.org/10.1007/978-3-030-22102-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-22102-7_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22101-0

  • Online ISBN: 978-3-030-22102-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation