Advertisement

Only-Knowing à la Halpern-Moses for Non-omniscient Rational Agents: A Preliminary Report

  • Dimitris Askounis
  • Costas D. Koutras
  • Christos Moyzes
  • Yorgos Zikos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8761)

Abstract

We investigate the minimal knowledge approach of Halpern-Moses ‘only knowing’ in the context of two syntactic variants of stable belief sets that aim in avoiding the unreasonably perfect omniscient agent modelled in R. Stalnaker’s original definition of a stable epistemic state. The ‘only knowing’ approach of J. Halpern and Y. Moses provides equivalent characterizations of ‘honest’ formulas and characterizes the epistemic state of an agent that has been told only a finite number of facts. The formal account of what it means for an agent to ‘only know a’ is actually based on ‘minimal’ epistemic states and is closely related to ground modal nonmonotonic logics. We examine here the behaviour of the HM-‘only knowing’ approach in the realm of the weak variants of stable epistemic states introduced recently by relaxing the positive or negative introspection context rules of Stalnaker’s definition, in a way reminiscent of the work done in modal epistemic logic in response to the ‘logical omniscience’ problem. We define the ‘honest’ formulas - formulas which can be meaningfully ‘only known’ - and characterize them in several ways, including model-theoretic characterizations using impossible worlds. As expected, the generalized ‘only knowing’ approach lacks the simplicity and elegance shared by the approaches based on Stalnaker’s stable sets (actually based on S5) but it is more realistic and can be handily fine-tuned.

Keywords

Only-knowing minimal knowledge modal nonmonotonic logic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ågotnes, T., Alechina, N.: The dynamics of syntactic knowledge. Journal of Logic and Computation 17(1), 83–116 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Belle, V., Lakemeyer, G.: Multi-agent only-knowing revisited. In: Lin, et al. (eds.) [26]Google Scholar
  3. 3.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press (2001)Google Scholar
  4. 4.
    Brewka, G., Eiter, T., McIlraith, S.A. (eds.): Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference, KR 2012, Rome, Italy, June 10-14, 2012. AAAI Press (2012)Google Scholar
  5. 5.
    Chellas, B.F.: Modal Logic, an Introduction. Cambridge University Press (1980)Google Scholar
  6. 6.
    Donini, F.M., Nardi, D., Rosati, R.: Ground nonmonotonic modal logics. Journal of Logic and Computation 7(4), 523–548 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fitting, M.C.: Basic Modal Logic. In: Gabbay, et al. (eds.) [8], vol. 1, pp. 368–448 (1993)Google Scholar
  8. 8.
    Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.): Handbook of Logic in Artificial Intelligence and Logic Programming. Oxford University Press (1993)Google Scholar
  9. 9.
    Gabbay, D.M., Woods, J.: Logic and the Modalities in the Twentieth Century. Handbook of the History of Logic, vol. 7. North-Holland (2006)Google Scholar
  10. 10.
    Gochet, P., Gribomont, P.: Epistemic logic. In: Gabbay, Woods (eds.) [9], vol. 7, pp. 99–195 (2006)Google Scholar
  11. 11.
    Halpern, J.: A critical reexamination of default logic, autoepistemic logic and only-knowing. Computational Intelligence 13(1), 144–163 (1993); A preliminary version appears in Mundici, D., Gottlob, G., Leitsch, A. (eds.): KGC 1993. LNCS, vol. 713, pp. 144–163. Springer, Heidelberg (1993)Google Scholar
  12. 12.
    Halpern, J.: A theory of knowledge and ignorance for many agents. Journal of Logic and Computation 7(1), 79–108 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Halpern, J., Moses, Y.: Towards a theory of knowledge and ignorance: Preliminary report in Apt, K. (ed.) Logics and Models of Concurrent Systems. Springer (1985)Google Scholar
  14. 14.
    Halpern, J.Y., Lakemeyer, G.: Multi-agent only knowing. Journal of Logic and Computation 11(1), 41–70 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Halpern, J.Y., Pucella, R.: Dealing with logical omniscience: Expressiveness and pragmatics. Artificial Intelligence 175(1), 220–235 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    van der Hoek, W., Jaspars, J., Thijsse, E.: Honesty in partial logic. Studia Logica 56(3), 323–360 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge (1996)Google Scholar
  18. 18.
    Jago, M.: Logics for Resource-Bounded Agents. PhD thesis, University of Nottingham (2006)Google Scholar
  19. 19.
    Janhunen, T., Niemelä, I. (eds.): JELIA 2010. LNCS, vol. 6341. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  20. 20.
    Jaspars, J.: A generalization of stability and its application to circumscription of positive introspective knowledge. In: Schönfeld, W., Börger, E., Kleine Büning, H., Richter, M.M. (eds.) CSL 1990. LNCS, vol. 533, pp. 289–299. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  21. 21.
    Koutras, C.D., Moyzes, C., Zikos, Y.: Syntactic reconstructions of stable belief sets. Technical report, Graduate Programme in Algorithms and Computation (2014)Google Scholar
  22. 22.
    Koutras, C.D., Zikos, Y.: On a modal epistemic axiom emerging from McDermott-Doyle logics. Fundamenta Informaticae 96(1-2), 111–125 (2009)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Koutras, C.D., Zikos, Y.: Stable belief sets revisited. In: Janhunen, Niemelä (eds.) [19], pp. 221–233Google Scholar
  24. 24.
    Lakemeyer, G., Levesque, H.J.: Only-knowing meets nonmonotonic modal logic. In: Brewka, et al. (eds.) [4]Google Scholar
  25. 25.
    Levesque, H.J.: All I Know: A study in autoepistemic logic. Artificial Intelligence 42(2-3), 263–309 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Lin, F., Sattler, U., Truszczynski, M. (eds.): Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference, KR 2010, Toronto, Ontario, Canada, May 9-13. AAAI Press (2010)Google Scholar
  27. 27.
    Marek, V.W., Schwarz, G.F., Truszczyński, M.: Modal non-monotonic logics: Ranges,characterization, computation. Journal of the ACM 40, 963–990 (1993)CrossRefzbMATHGoogle Scholar
  28. 28.
    Marek, V.W., Truszczyński, M.: Nonmonotonic Logic: Context-dependent Reasoning. Springer (1993)Google Scholar
  29. 29.
    Pearce, D., Uridia, L.: An approach to minimal belief via objective belief. In: Walsh (ed.) [34], pp. 1045–1050Google Scholar
  30. 30.
    Schwarz, G.F., Truszczyński, M.: Minimal knowledge problem: a new approach. Artificial Intelligence 67, 113–141 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Segerberg, K.: An essay in Clasical Modal Logic. Filosofiska Studies, Uppsala (1971)Google Scholar
  32. 32.
    Stalnaker, R.: A note on non-monotonic modal logic. Artificial Intelligence 64, 183–196 (1993) (Revised version of the unpublished note originally circulated in 1980)MathSciNetCrossRefGoogle Scholar
  33. 33.
    van der Hoek, W., Jaspars, J., Thijsse, E.: Persistence and minimality in epistemic logic. Annals of Mathematics and Artificial Intelligence 27(1-4), 25–47 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Walsh, T. (ed.): Proceedings of the 22nd International Joint Conference on Artificial Intelligence, IJCAI 2011, Barcelona, Catalonia, Spain, July 16-22. IJCAI/AAAI (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dimitris Askounis
    • 1
  • Costas D. Koutras
    • 2
  • Christos Moyzes
    • 3
  • Yorgos Zikos
    • 3
  1. 1.Decision Support Systems Lab, School of Electrical and Comp. EngineeringNational Technical University of AthensAthensGreece
  2. 2.Department of Informatics and TelecommunicationsUniversity of PeloponneseTripolisGreece
  3. 3.Graduate Programme in Logic, Algorithms and Computation (MPLA) Department of MathematicsUniversity of AthensIlissiaGreece

Personalised recommendations