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Seeing Is Believing: Formalising False-Belief Tasks in Dynamic Epistemic Logic

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Jaakko Hintikka on Knowledge and Game-Theoretical Semantics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 12))

Abstract

In this paper we show how to formalise false-belief tasks like the Sally-Anne task and the second-order chocolate task in Dynamic Epistemic Logic (DEL). False-belief tasks are used to test the strength of the Theory of Mind (ToM) of humans, that is, a human’s ability to attribute mental states to other agents. Having a ToM is known to be essential to human social intelligence, and hence likely to be essential to social intelligence of artificial agents as well. It is therefore important to find ways of implementing a ToM in artificial agents, and to show that such agents can then solve false-belief tasks. In this paper, the approach is to use DEL as a formal framework for representing ToM, and use reasoning in DEL to solve false-belief tasks. In addition to formalising several false-belief tasks in DEL, the paper introduces some extensions of DEL itself: edge-conditioned event models and observability propositions. These extensions are introduced to provide better formalisations of the false-belief tasks, but expected to have independent future interest.

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Notes

  1. 1.

    One might argue that if Sally is capable of doing intention recognition, that is, predict the goals of Anne, she might actually suspect that Anne has been transferring the marble while she was away, because she perhaps knows that Anne wants the marble for herself. However, it is implicit in the Sally-Anne task that intention recognition is not taken into account, and we will not do it here either.

  2. 2.

    Except if the tested agent itself ends up forming a false belief. For instance, in the case of the Sally-Anne task, an agent without a ToM could in principle pass the test by being fooled into itself believing that the marble is in the basket. When asked about where Sally believes the marble to be, the agent would consult its own beliefs, and answer “in the basket”. But often in the Sally-Anne task, two questions are asked: “where is the marble?” and “where does Sally believe the marble to be”. To pass the test, the answers to the two questions must be distinct.

  3. 3.

    Strictly speaking, we should say “John believes this” instead of “John knows this”, since our modality is a belief modality. To improve readability, we however allow ourselves to slightly abuse the term and use “knows” instead of “believes” when the formula believed is also true.

  4. 4.

    Note that all states considered so far in this paper have been functional, and that the property of being functional is preserved under any sequence of updates with \(do(i,\phi )\) and \(oc(\phi )\) actions.

References

  1. Premack D, Woodruff G (1978) Does the chimpanzee have a theory of mind? Beh Brain Sci 1(4):515–526

    Google Scholar 

  2. Wimmer H, Perner J (1983) Beliefs about beliefs: representation and constraining function of wrong beliefs in young children’s understanding of deception. Cognition 13(1):103–128

    Article  Google Scholar 

  3. Frith U (1989). Autism: explaining the enigma. Wiley

    Google Scholar 

  4. Baron-Cohen S, Leslie AM (1985) Does the autistic child have a theory of mind? Cognition 21(1):37–46

    Article  Google Scholar 

  5. Hintikka J (1962) Knowledge and belief: an introduction to the logic of the two notions. Cornell University Press

    Google Scholar 

  6. Van Ditmarsch H, Labuschagne W (2007) My beliefs about your beliefs: a case study in theory of mind and epistemic logic. Synthese 155(2):191–209

    Article  Google Scholar 

  7. Aucher G (2012) Private announcement and belief expansion: an internal perspective. J Log Comput 22(3):451–479

    Article  Google Scholar 

  8. Stenning K, van Lambalgen M (2008) Human reasoning and cognitive science. MIT Press

    Google Scholar 

  9. Wahl S, Spada H (2000) Childrens reasoning about intentions, beliefs and behaviour. Cognitive Sci Q 1(1):3–32

    Google Scholar 

  10. Arkoudas K, Bringsjord S (2008) Toward formalizing common-sense psychology: an analysis of the false-belief task. In: Ho TB, Zhou Z-H (eds) PRICAI, volume 5351 of lecture notes in computer science. Springer, pp 17–29

    Google Scholar 

  11. Breazeal C, Gray J, Berin M (2011) Mindreading as a foundational skill for socially intelligent robots. In: Robotics research. Springer, pp 383–394

    Google Scholar 

  12. Sindlar MP (2011) In the eye of the beholder: explaining behavior through mental state attribution. PhD thesis, Universiteit Utrecht

    Google Scholar 

  13. Arslan B, Taatgen N, Verbrugge R (2013) Modeling developmental transitions in reasoning about false beliefs of others. In: Proceedings of the 12th international conference on cognitive modelling

    Google Scholar 

  14. Braüner T (2013) Hybrid-logical reasoning in false-belief tasks. In Schipper BC (ed) Proceedings of fourteenth conference on theoretical aspects of rationality and knowledge (TARK), pp 186–195

    Google Scholar 

  15. Verbrugge R (2009) Logic and social cognition. J Philos Log 38(6):649–680

    Article  Google Scholar 

  16. Ghosh S, Meijering B, Verbrugge R (2014) Strategic reasoning: building cognitive models from logical formulas. J Log Lang Inf 23(1):1–29

    Article  Google Scholar 

  17. Bolander T, Andersen MB (2011) Epistemic planning for single- and multi-agent systems. J Appl Non-Class Log 21:9–34

    Article  Google Scholar 

  18. van Ditmarsch H, Kooi B (2008) Semantic results for ontic and epistemic change. In: Bonanno G, van der Hoek W, Wooldridge M (eds) Logic and the foundation of game and decision theory (LOFT 7), texts in logic and games 3. Amsterdam University Press, pp 87–117

    Google Scholar 

  19. Baltag A, Moss L (2004) Logic for epistemic programs. Synthese 139(2):165–224

    Article  Google Scholar 

  20. Baltag A, Moss LS, Solecki S (1998) The logic of public announcements and common knowledge and private suspicions. In: Gilboa I (ed) Proceedings of the 7th conference on theoretical aspects of rationality and knowledge (TARK-98). Morgan Kaufmann, pp 43–56

    Google Scholar 

  21. van Benthem J, van Eijck J, Kooi B (2006) Logics of communication and change. Inf Comput 204(11):1620–1662

    Article  Google Scholar 

  22. van Ditmarsch H, van der Hoek W, Kooi B (2005) Dynamic epistemic logic with assignment. In Dignum F, Dignum V, Koenig S, Kraus S, Singh MP, Wooldridge M (eds) Autonomous agents and multi-agent systems (AAMAS 2005). ACM, pp 141–148

    Google Scholar 

  23. van Ditmarsch H, Herzig A, Lorini E, Schwarzentruber F (2013) Listen to me! public announcements to agents that pay attention—or not. In: Logic, rationality, and interaction. Springer, pp 96–109

    Google Scholar 

  24. Bolander T, van Ditmarsch H, Herzig A, Lorini E, Pardo P, Schwarzentruber F (2015) Announcements to attentive agents. J Log Lang Inf, pp 1–35

    Google Scholar 

  25. Lorini E, Tummolini L, Herzig A (2005) Establishing mutual beliefs by joint attention: towards a formal model of public events. In: Proceedings of CogSci. pp 1325–1330

    Google Scholar 

  26. Tomasello M (1995) Joint attention as social cognition. In: Joint attention: its origins and role in development, pp 103–130

    Google Scholar 

  27. Flobbe L, Verbrugge R, Hendriks P, Krämer I (2008) Childrens application of theory of mind in reasoning and language. J. Log Lang Inf, 17 (4): 417–442. Special issue on formal models for real people, Counihan M (ed)

    Google Scholar 

  28. Josef P, Heinz W (1985) John thinks that Mary thinks that attribution of second-order beliefs by 5–10-year-old children. J Exp Child Psy 39(3):437–471

    Google Scholar 

  29. Sullivan K, Zaitchik D, Tager-Flusberg H (1994) Preschoolers can attribute second-order beliefs. Dev Psychol 30(3):395

    Article  Google Scholar 

  30. Baltag A, Smets S (2008) A qualitative theory of dynamic interactive belief revision. In Bonanno G, van der Hoek W, Wooldridge M (eds) Logic and the foundations of game and decision theory (LOFT7), volume 3 of texts in logic and games. Amsterdam University Press, pp 13–60

    Google Scholar 

  31. Baral C, Gelfond G, Pontelli E, Son TC (2012) An action language for reasoning about beliefs in multi-agent domains. In: Proceedings of the 14th international workshop on non-monotonic reasoning, vol 4

    Google Scholar 

  32. Brenner M, Nebel B (2009) Continual planning and acting in dynamic multiagent environments. Auton Agents Multi-Agent Syst 19(3):297–331

    Article  Google Scholar 

  33. Herzig A, Lorini E, Maffre F (2015) A poor mans epistemic logic based on propositional assignment and higher-order observation. In: Logic, rationality and interaction. Lecture notes in computer science, vol 9394. Springer

    Google Scholar 

  34. van der Hoek W, Troquard N, Wooldridge M (2011) Knowledge and control. In: The 10th international conference on autonomous agents and multiagent systems. International foundation for autonomous agents and multiagent systems, vol 2. pp 719–726

    Google Scholar 

  35. Seligman J, Liu F, Girard P (2013) Facebook and the epistemic logic of friendship. In: Schipper BC (ed) Proceedings of fourteenth conference on theoretical aspects of rationality and knowledge (TARK), pp 229–238

    Google Scholar 

  36. Kooi B, Renne B (2011) Generalized arrow update logic. In: Proceedings of the 13th conference on theoretical aspects of rationality and knowledge. ACM, pp 205–211

    Google Scholar 

  37. Andersen MB, Bolander T, Jensen MH (2012) Conditional epistemic planning. Lect Notes Artif Intell 7519: 94–106. Proceedings of JELIA 2012

    Google Scholar 

  38. Bolander T (2014) Seeing is believing: Formalising false-belief tasks in dynamic epistemic logic. In: Herzig A, Lorini E (eds) Proceedings of the European conference on social intelligence (ECSI-2014), volume 1283 of CEUR workshop proceedings, pp 87–107. https://www.CEUR-WS.org

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Acknowledgements

This paper is an extended and revised version of a paper presented at the first European Conference on Social Intelligence (ECSI) in Barcelona, 2014 [38]. The author wishes to thank Patrick Blackburn and the anonymous reviewers of both the original submission and this extended version for their encouraging feedback and their many helpful comments and suggestions. The author is also very grateful to the editors of this volume for the invitation to contribute. The author acknowledges support from the Carlsberg Foundation (Center for Information and Bubble Studies, CIBS).

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  1. Technical University of Denmark, Richard Petersens Plads, Building 324, 2800, Lyngby, Denmark

    Thomas Bolander

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  1. Thomas Bolander
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Correspondence to Thomas Bolander .

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  1. LORIA, CNRS, Université de Lorraine, Vandoeuvre-lès-Nancy, France

    Hans van Ditmarsch

  2. Department of Philosophy, University of Helsinki, Helsinki, Finland

    Gabriel Sandu

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Bolander, T. (2018). Seeing Is Believing: Formalising False-Belief Tasks in Dynamic Epistemic Logic. In: van Ditmarsch, H., Sandu, G. (eds) Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. Outstanding Contributions to Logic, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-62864-6_8

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