An Epistemic Approach to Nondeterminism: Believing in the Simplest Course of Events

  • James P. DelgrandeEmail author
  • Hector J. Levesque


This paper describes an approach for reasoning in a dynamic domain with nondeterministic actions in which an agent’s (categorical) beliefs correspond to the simplest, or most plausible, course of events consistent with the agent’s observations and beliefs. The account is based on an epistemic extension of the situation calculus, a first-order theory of reasoning about action that accommodates sensing actions. In particular, the account is based on a qualitative theory of nondeterminism. Our position is that for commonsense reasoning, the world is most usefully regarded as deterministic, and that nondeterminism is an epistemic phenomenon, arising from an agent’s limited awareness and perception. The account offers several advantages: an agent has a set of categorical (as opposed to probabilistic) beliefs, yet can deal with equally-likely outcomes (such as in flipping a fair coin) or with outcomes of differing plausibility (such as an action that on rare occasions may fail). The agent maintains as its set of contingent beliefs the most plausible, or simplest, picture of the world, consistent with its beliefs and actions it believes it executed; yet it may modify these in light of later information.


Knowledge representation and reasoning Reasoning about action Nondeterminism 


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  1. 1.
    Alchourrón, C.E., P. Gärdenfors, and D. Makinson, On the logic of theory change: Partial meet contraction and revision functions, Journal of Symbolic Logic 50(2): 510–530, 1985.CrossRefGoogle Scholar
  2. 2.
    Bacchus, F., J.Y. Halpern, and H.J. Levesque, Reasoning about noisy sensors and effectors in the situation calculus, Artificial Intelligence 111(1–2): 171–208, 1999.CrossRefGoogle Scholar
  3. 3.
    Baral, C., Reasoning about actions: Non-deterministic effects, constraints, and qualification, in Proceedings of the International Joint Conference on Artificial Intelligence, Montréal, Canada, 1995, pp. 2017–2026.Google Scholar
  4. 4.
    Boutilier, C., R. Reiter, M. Soutchanski, and S. Thrun, Decision-theoretic, high-level agent programming in the situation calculus, in Proceedings of the (AAAI) Conference on Artificial Intelligence, Austin, TX, 2000, pp. 355–362.Google Scholar
  5. 5.
    Cimatti, A., M. Pistore, M. Roveri, and P. Traverso, Weak, strong, and strong cyclic planning via symbolic model checking, Artificial Intelligence 147(1–2): 35–84, 2003.CrossRefGoogle Scholar
  6. 6.
    Darwiche, A., and J. Pearl, On the logic of iterated belief revision, Artificial Intelligence 89: 1–29, 1997.CrossRefGoogle Scholar
  7. 7.
    Delgrande, J.P., and H.J. Levesque, Belief revision with sensing and fallible actions, in Thirteenth International Conference on Principles of Knowledge Representation and Reasoning, Rome, Italy, 2012.Google Scholar
  8. 8.
    Delgrande, J.P., and H.J. Levesque, A formal account of nondeterministic and failed actions, in Proceedings of the International Joint Conference on Artificial Intelligence, Beijing, China, 2012.Google Scholar
  9. 9.
    Fikes, R.F., and N.J. Nilsson, Strips: A new approach to the application of theorem proving to problem solving, Artificial Intelligence 2: 189–208, 1971.CrossRefGoogle Scholar
  10. 10.
    Gärdenfors, P., Knowledge in Flux: Modelling the Dynamics of Epistemic States, The MIT Press, Cambridge, MA, 1988.Google Scholar
  11. 11.
    Gelfond, M., and V. Lifschitz, Action languages, Electronic Transactions on AI, 3, 1998.Google Scholar
  12. 12.
    Ginsberg, M.L., and D.E. Smith, Reasoning about action ii: The qualification problem, Artificial Intelligence 35(3): 311–342, 1988.CrossRefGoogle Scholar
  13. 13.
    Jensen, R.M., M.M. Veloso, and R.E. Bryant, Fault tolerant planning: Toward probabilistic uncertainty models in symbolic non-deterministic planning, in S. Zilberstein, J. Koehler, and S. Koenig, (eds.), Proceedings of the Fourteenth International Conference on Automated Planning and Scheduling (ICAPS 2004), AAAI Press, 2004, pp. 335–344.Google Scholar
  14. 14.
    Katsuno, H., and A. Mendelzon, Propositional knowledge base revision and minimal change, Artificial Intelligence 52(3): 263–294, 1991.CrossRefGoogle Scholar
  15. 15.
    Laplace, P., Essai philosophique sur les probabilités, first edn., (English trans: Dover, 1952), Paris, 1814.Google Scholar
  16. 16.
    Levesque, H.J., F. Pirri, and R. Reiter, Foundations for the situation calculus, Linköping Electronic Articles in Computer and Information Science 3: 18, 1998.Google Scholar
  17. 17.
    Levesque, H.J., R. Reiter, F. Lin, and R.B. Scherl, Golog: A logic programming language for dynamic domains, Journal of Logic Programming 31: 59–83, 1997.CrossRefGoogle Scholar
  18. 18.
    McCarthy, J., Epistemological problems in artificial intelligence, in Proceedings of the International Joint Conference on Artificial Intelligence, Cambridge, MA, 1977, pp. 1038–1044.Google Scholar
  19. 19.
    Moore, R.C., Semantical considerations on nonmonotonic logic, Artificial Intelligence 25: 75–94, 1985.CrossRefGoogle Scholar
  20. 20.
    Peppas, P., Belief revision, in F. van Harmelen, V. Lifschitz, and B. Porter, (eds.), Handbook of Knowledge Representation, Elsevier Science, San Diego, USA, 2008, pp. 317–359.CrossRefGoogle Scholar
  21. 21.
    Pratt, V., Semantical considerations on Floyd-Hoare logic, in 17th IEEE Symposium on Foundations of Computer Science, 1976, pp. 109–121.Google Scholar
  22. 22.
    Reiter, R., Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems, The MIT Press, Cambridge, MA, 2001.Google Scholar
  23. 23.
    Scherl, R.B., and H.J. Levesque, Knowledge, action, and the frame problem, Artificial Intelligence 144(1–2): 1–39, 2003.CrossRefGoogle Scholar
  24. 24.
    Shanahan, M., Solving the frame problem - a mathematical investigation of the common sense law of inertia, MIT Press, 1997.Google Scholar
  25. 25.
    Shapiro, S., M. Pagnucco, Y. Lespérance, and H.J. Levesque, Iterated belief change in the situation calculus, Artificial Intelligence 175(1): 165–192, 2011.CrossRefGoogle Scholar
  26. 26.
    Spohn, W., Ordinal conditional functions: A dynamic theory of epistemic states, in W.L. Harper, and B. Skyrms, (eds.), Causation in Decision, Belief Change, and Statistics, vol. II, Kluwer Academic Publishers, 1988, pp. 105–134.Google Scholar
  27. 27.
    Thielscher, M., The qualification problem: A solution to the problem of anomalous models, Artificial Intelligence 131(1–2): 1–37, 2001.CrossRefGoogle Scholar

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada

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