, Volume 155, Issue 2, pp 191–209 | Cite as

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

Original Paper


We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.


Belief revision Modal logic Dynamic epistemic logic Preferences 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Asheim G.B., Søvik Y. (2005). Preference-based belief operators. Mathematical Social Sciences 50(1): 61–82Google Scholar
  2. Aucher, G. (2003). A combined system for update logic and belief revision. Master’s thesis, ILLC, University of Amsterdam, Amsterdam, The Netherlands.Google Scholar
  3. Baltag, A., & Moss, L. S. (2004). Logics for epistemic programs. Synthese, 139, 165–224. Knowledge, Rationality and Action, 1–60.Google Scholar
  4. Baltag, A., & Smets, S. (2006). Dynamic belief revision over multi-agent plausibility models. Proceedings of LOFT 2006 (7th conference on logic and the foundations of game and decision theory). University of Liverpool.Google Scholar
  5. Baron-Cohen S. (1995) Mindblindness: An essay on autism and theory of mind. Cambridge, MA, MIT PressGoogle Scholar
  6. Baron-Cohen S., Leslie A.M., Frith U. (1985). Does the autistic child have a ‘theory of mind’?. Cognition 21, 37–46CrossRefGoogle Scholar
  7. Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press. Cambridge Tracts in Theoretical Computer Science 53.Google Scholar
  8. Board O. (2004). Dynamic interactive epistemology. Games and Economic Behaviour 49, 49–80CrossRefGoogle Scholar
  9. Cleckley, H. (1976). The mask of sanity. St Louis, MO: Mosby. Available as http://www.cassiopaea. org/cass/sanity_1.pdf.Google Scholar
  10. Ferguson, D., & Labuschagne, W. A. (2002). Information-theoretic semantics for epistemic logic. In Proceedings of LOFT 5, Turin, Italy. ICER. no page numbers.Google Scholar
  11. Frith C.D., Frith U. (1999). Interacting minds—a biological basis. Science 286: 1692–1695CrossRefGoogle Scholar
  12. Gallese V., Goldman A. (1998). Mirror neurons and the simulation theory of mind-reading. Trends in Cognitive Sciences 12, 493–501CrossRefGoogle Scholar
  13. Halpern J.Y. (2003). Reasoning about uncertainty. Cambridge, MA, MIT PressGoogle Scholar
  14. Hare R.D. (1993). Without conscience. New York, The Guilford PressGoogle Scholar
  15. Kraus S., Lehmann D. (1988). Knowledge, belief and time. Theoretical Computer Science 58, 155–174CrossRefGoogle Scholar
  16. Kraus S., Lehmann D., Magidor M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–207CrossRefGoogle Scholar
  17. Lewis D.K. (1969). Convention, a philosophical study. Cambridge (MA), Harvard University PressGoogle Scholar
  18. Lewis D.K. (1973). Counterfactuals. Cambridge (MA), Harvard University PressGoogle Scholar
  19. Lindström S., Rabinowicz W. (1999). DDL unlimited: Dynamic doxastic logic for introspective agents. Erkenntnis 50, 353–385CrossRefGoogle Scholar
  20. Lomuscio, A. R. (1999). Knowledge sharing among ideal agents. Ph.D Thesis, University of Birmingham, Birmingham, UK.Google Scholar
  21. Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z. W. Ras (Eds.), Proceedings of the 4th international symposium on methodologies for intelligent systems (pp. 201–216). Oak Ridge: Oak Ridge National Laboratory.Google Scholar
  22. Premack D., Woodruff G. (1978). Does the chimpanzee have a ‘theory of mind’?. Behavioral and Brain Sciences 4, 515–526CrossRefGoogle Scholar
  23. Rao, A. S., & Georgeff, M. P. (1991). Modeling rational agents within a BDI-architecture. In J. Allen, R. Fikes, & E. Sandewall (Eds.), Proceedings of the 2nd international conference on principles of knowledge representation and reasoning (KR ’91) (pp. 473–484). San Mateo (CA): Morgan Kaufmann.Google Scholar
  24. Rott, H. (2004). Adjusting priorities: Simple representations for 27 iterated theory change operators. In H. Langerlund, S. Lindström, & R. Sliwinski (Eds.), Modality matters: Twenty-five essays in honour of Krister Segerberg (pp. 359–384).Google Scholar
  25. Segerberg K. (1999). Two traditions in the logic of belief: bringing them together. In: Ohlbach H.J., Reyle U.(eds) Logic, language, and reasoning. Dordrecht, Kluwer Academic Publishers, pp. 135–147Google Scholar
  26. Sodian B., Frith U. (1992). Deception and sabotage in autistic, retarded, and normal children. Journal of Child Psychology and Psychiatry 33, 591–606CrossRefGoogle Scholar
  27. Spohn W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states. In: Harper W.L., Skyrms B.(eds) Causation in decision, belief change, and statistics vol. II. Dordrecht, Kluwer, pp. 105–134Google Scholar
  28. Stalnaker R. (1996). Knowledge, belief and counterfactual reasoning in games. Economics and Philosophy 12, 133–163CrossRefGoogle Scholar
  29. Stenning K., van Lambalgen M. (2006). Human Reasoning and Cognitive Science. Cambridge, MA: MIT University PressGoogle Scholar
  30. van Benthem J.F.A.K. (1998). Dynamic odds and ends. Technical report, University of Amsterdam. ILLC Research Report ML-1998-08Google Scholar
  31. van Benthem, J. F. A. K. (2006). Dynamic logic for belief change. Journal of Applied Non-Classical Logics, 14.Google Scholar
  32. van Benthem, J. F. A. K., & Liu, F. (2005). Dynamic logic of preference upgrade. Technical report, University of Amsterdam. ILLC Research Report PP-2005-29.Google Scholar
  33. van der Hoek W. (1993). Systems for knowledge and beliefs. Journal of Logic and Computation 3(2): 173–195CrossRefGoogle Scholar
  34. van Ditmarsch H.P. (2005). Prolegomena to dynamic logic for belief revision. Synthese (Knowledge, Rationality & Action) 147: 229–275Google Scholar
  35. van Ditmarsch, H. P., & Labuschagne, W. A. (2003). A multimodal language for revising defeasible beliefs. In E. Álvarez, R. Bosch, & L. Villamil (Eds.), Proceedings of the 12th international congress of logic, methodology, and philosophy of science (LMPS) (pp. 140–141). Oviedo University Press.Google Scholar
  36. van Lambalgen M., Smid H. (2003). Reasoning patterns in autism: rules and exceptions. In Perez Miranda L.A., Larrazabal J.M.(eds) Proceedings of the eighth international colloquium on cognitive science. Dordrecht, Kluwer Science PublishersGoogle Scholar
  37. Voorbraak, F. P. J. M. (1993). As far as I know. Ph.D thesis, Utrecht University, Utrecht, NL. Questiones Infinitae volume VII.Google Scholar
  38. Wimmer H., Perner J. (1983). Beliefs about beliefs: Representation and constraining function of wrong beliefs in young children’s understanding of deception. Cognition 13, 103–128CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.University of OtagoDunedinNew Zealand

Personalised recommendations