Skip to main content
SpringerLink
Log in

Towards a Logical Formalisation of Theory of Mind: A Study on False Belief Tasks

  • Conference paper
  • First Online:
Logic, Rationality, and Interaction (LORI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11813))

Included in the following conference series:

  • 748 Accesses

Abstract

Theory of Mind, the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes a mental attribution modelling logical framework that is more in-line with findings in cognitive science. We introduce the setting and some of its technical features, and argue why it does justice to empirical observations, using it for modelling well-known False-Belief Tasks.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

Notes

  1. 1.

    There has been a debate on how this understanding of others’ mental states is achieved (see, e.g., [2]). Some argue that it is by acquiring a theory of commonsense psychology (theory theory); some others argue that it comes from a direct simulation of others’ mental states (simulation theory). We will use the term ToM without endorsing any of these views, as such discussion falls outside the scope of this proposal.

  2. 2.

    Frameworks for representing acts of private communication [11] make this clear. Their additional structures, action models, have one ‘event’ for each different perspective the agents might have about the communication, and the model after the communication contains roughly one copy of the original model for each one of these perspectives.

  3. 3.

    Anti-Psychologism (e.g., [12]) has long been against attempts to reconcile the two [13].

  4. 4.

    In particular, one goal is to find a system that provides a plausible answer on why people find mental attribution tasks increasingly difficult as their order increases.

  5. 5.

    Following the common parlance in the literature describing the tasks we later model, the term belief will be used for referring to an agent’s mental state.

  6. 6.

    Each object has a proper colour: \(\kappa _s(o) \in R_o\) holds for all \(s \in S\) and \(o \in O\).

  7. 7.

    Every agent can see herself in every state: \(a \in \nu _s(a)\) holds for all \(s \in S\) and all \(a \in A\).

  8. 8.

    In particular, \([s]_{-0} = s\). Note also how \([s]_{-t}\) is undefined for \(t > \tau (s)\).

  9. 9.

    Notice that visibility of each agent is not ‘common knowledge’: knowledge relies on visibility, and an agent can see without being seen (Subsect. 3.1). Additionally, our simplifying assumption might be a problem for attributions under (semi-)private actions. Work of [22, 23] can be especially relevant in that respect.

  10. 10.

    Note: a single ‘predecessor’ modality is insufficient, as the number of back steps the recursive exploration requires is a priori unknown. A modality for its reflexive and transitive closure is still not enough: it takes care of the recursive search for a state satisfying the visibility condition, but on its own cannot indicate that every state up to that point should not satisfy it. More on the adequacy of since can be found in [27].

  11. 11.

    Within propositional dynamic logic [29], and in the presence of the converse , the since modality can be defined as , with “” indicating relational test, “” indicating sequential composition, “” indicating non-deterministic choice, and “” indicating one or more iterations.

  12. 12.

    Since \(\mathcal {L'}\)-formulas are evaluated with respect to a TV model’s last state, it is enough for a bisimulation to establish a connection between those states, as the definition does.

  13. 13.

    In fact, unsuccessful performance, e.g. of autistic children, is often connected with a failure in perspective shifting, resulting in the subject reporting her own beliefs [6, 33].

  14. 14.

    Although it is always possible to evaluate attributions of any length (like in possible-worlds semantics), our semantic clause offers a mechanism to account for human reasoning limitations, indicated by empirical research, e.g. on working memory [38]. It allows us to trace how many states need to be held in working memory, and therefore explain why attribution-making might fail from some point on.

  15. 15.

    For example, the act through which, in the absence of Sally, Anne moves the marble from the basket to the box, is understood as a private announcement through which only Anne is informed about the marble’s new location.

References

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

    Article  Google Scholar 

  2. Carruthers, P., Smith, P.K.: Theories of Theories of Mind. Cambridge University Press, Cambridge (1996)

    Book  Google Scholar 

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

    Article  Google Scholar 

  4. Wellman, H.M.: From desires to beliefs: acquisition of a theory of mind. In: Natural Theories of Mind: Evolution, Development and Simulation of Everyday Mindreading, pp. 19–38. Basil Blackwell, Cambridge (1991)

    Google Scholar 

  5. Baron-Cohen, S., Leslie, A.M., Frith, U.: Does the autistic child have a “theory of mind”? Cognition 21(1), 37–46 (1985)

    Article  Google Scholar 

  6. Stenning, K., van Lambalgen, M.: Human Reasoning and Cognitive Science. MIT Press, Cambridge (2008)

    Book  Google Scholar 

  7. Setoh, P., Scott, R.M., Baillargeon, R.: Two-and-a-half-year-olds succeed at a traditional false-belief task with reduced processing demands. Proc. Natl. Acad. Sci. 113(47), 13360–13365 (2016)

    Article  Google Scholar 

  8. Hintikka, J.: Knowledge and Belief. Cornell University Press, Ithaca (1962)

    MATH  Google Scholar 

  9. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. The MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  10. Stalnaker, R.: The problem of logical omniscience, I. Synthese 89(3), 425–440 (1991)

    Article  MathSciNet  Google Scholar 

  11. Baltag, A., Moss, L.S., Solecki, S.: 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 1998), Evanston, IL, USA, 22–24 July 1998, pp. 43–56. Morgan Kaufmann (1998)

    Google Scholar 

  12. Frege, G.: Grundlagen der Arithmetik. Wilhelm Koebner, Breslau (1884)

    Google Scholar 

  13. Pelletier, F.J., Elio, R., Hanson, P.: Is logic all in our heads? From naturalism to psychologism. Stud. Logica 88(1), 3–66 (2008)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. van Benthem, J.: Logic and reasoning: do the facts matter? Stud. Logica 88(1), 67–84 (2008)

    Article  MathSciNet  Google Scholar 

  16. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library Series, vol. 337. Springer, Dordrecht (2008). https://doi.org/10.1007/978-1-4020-5839-4

    Book  MATH  Google Scholar 

  17. van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, New York (2011)

    Book  Google Scholar 

  18. Yap, A.: Dynamic epistemic logic and temporal modality. In: Girard, P., Roy, O., Marion, M. (eds.) Dynamic Formal Epistemology. Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science), vol. 351, pp. 33–50. Springer, Dordrecht (2011). https://doi.org/10.1007/978-94-007-0074-1_3

    Chapter  MATH  Google Scholar 

  19. Sack, J.: Temporal languages for epistemic programs. J. Logic Lang. Inf. 17(2), 183–216 (2008)

    Article  MathSciNet  Google Scholar 

  20. Renne, B., Sack, J., Yap, A.: Logics of temporal-epistemic actions. Synthese 193(3), 813–849 (2016)

    Article  MathSciNet  Google Scholar 

  21. Baltag, A., Özgün, A., Vargas Sandoval, A.L.: APAL with memory is better. In: Moss, L.S., de Queiroz, R., Martinez, M. (eds.) WoLLIC 2018. LNCS, vol. 10944, pp. 106–129. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-662-57669-4_6

    Chapter  Google Scholar 

  22. Gasquet, O., Goranko, V., Schwarzentruber, F.: Big brother logic: visual-epistemic reasoning in stationary multi-agent systems. Auton. Agents Multi Agent Syst. 30(5), 793–825 (2016)

    Article  Google Scholar 

  23. Charrier, T., Herzig, A., Lorini, E., Maffre, F., Schwarzentruber, F.: Building epistemic logic from observations and public announcements. In: Proceedings of the Fifteenth International Conference on Principles of Knowledge Representation and Reasoning, KR 2016, pp. 268–277. AAAI Press (2016)

    Google Scholar 

  24. Reiter, R.: A logic for default reasoning. Artif. Intell. 13(1–2), 81–132 (1980)

    Article  MathSciNet  Google Scholar 

  25. Ben-David, S., Ben-Eliyahu-Zohary, R.: A modal logic for subjective default reasoning. Artif. Intell. 116(1–2), 217–236 (2000)

    Article  MathSciNet  Google Scholar 

  26. Blackburn, P., de Rijke, M., Venema, Y.: Modal logic. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  27. Kamp, H.: Tense logic and the theory of linear order. Ph.D. thesis, University of California (1968)

    Google Scholar 

  28. Burgess, J.P.: Axioms for tense logic. I. “since” and “until”. Notre Dame J. Formal Logic 23(4), 367–374 (1982)

    Article  MathSciNet  Google Scholar 

  29. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)

    Book  Google Scholar 

  30. Kurtonina, N., De Rijke, M.: Bisimulations for temporal logic. J. Logic Lang. Inf. 6(4), 403–425 (1997)

    Article  MathSciNet  Google Scholar 

  31. Gärdenfors, P.: Knowledge in Flux. Modelling the Dynamics of Epistemic States. MIT Press, Cambridge (1988)

    MATH  Google Scholar 

  32. Braüner, T.: Hybrid-logical reasoning in the smarties and Sally-Anne tasks. J. Logic Lang. Inf. 23(4), 415–439 (2014)

    Article  MathSciNet  Google Scholar 

  33. Braüner, T.: Hybrid-logical reasoning in the smarties and Sally-Anne tasks: what goes wrong when incorrect responses are given? In: Proceedings of the 37th Annual Meeting of the Cognitive Science Society, Pasadena, California, USA, pp. 273–278. Cognitive Science Society (2015)

    Google Scholar 

  34. Braüner, T., Blackburn, P., Polyanskaya, I.: Second-order false-belief tasks: analysis and formalization. In: Väänänen, J., Hirvonen, Å., de Queiroz, R. (eds.) WoLLIC 2016. LNCS, vol. 9803, pp. 125–144. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52921-8_9

    Chapter  MATH  Google Scholar 

  35. Kahneman, D.: Thinking, Fast and Slow. Farrar, Straus and Giroux, New York (2011)

    Google Scholar 

  36. Evans, J.: Dual process theories. In: Ball, L., Thompson, V. (eds.) The Routledge International Handbook of Thinking and Reasoning, pp. 151–164. Routledge, London (2018)

    Google Scholar 

  37. Stanovich, K.E., West, R.F.: Individual differences in reasoning: implications for the rationality debate? Behav. Brain Sci. 23(5), 645–665 (2000)

    Article  Google Scholar 

  38. Cowan, N.: The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behav. Brain Sci. 24, 87–114 (2001)

    Article  Google Scholar 

  39. Flobbe, L., Verbrugge, R., Hendriks, P., Krämer, I.: Children’s application of theory of mind in reasoning and language. J. Logic Lang. Inf. 17(4), 417–442 (2008)

    Article  MathSciNet  Google Scholar 

  40. Perner, J., Wimmer, H.: “John Thinks that Mary Thinks that...” attribution of second-order beliefs by 5- to 10-year-old children. J. Exp. Child Psychol. 39(3), 437–471 (1985)

    Article  Google Scholar 

  41. Sullivan, K., Zaitchik, D., Tager-Flusberg, H.: Preschoolers can attribute second-order beliefs. Dev. Psychol. 30, 395–402 (1994)

    Article  Google Scholar 

  42. Hollebrandse, B., van Hout, A., Hendriks, P.: Children’s first and second-order false-belief reasoning in a verbal and a low-verbal task. Synthese 191(3), 321–333 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  44. Bolander, T.: 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. OCL, vol. 12, pp. 207–236. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-62864-6_8

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands

    Anthia Solaki & Fernando R. Velázquez-Quesada

Authors
  1. Anthia Solaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fernando R. Velázquez-Quesada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Anthia Solaki or Fernando R. Velázquez-Quesada .

Editor information

Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Patrick Blackburn

  2. Université Paul Sabatier, IRIT-CNRS, Toulouse, France

    Emiliano Lorini

  3. Southwest University, Chongqing, China

    Meiyun Guo

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag GmbH Germany, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Solaki, A., Velázquez-Quesada, F.R. (2019). Towards a Logical Formalisation of Theory of Mind: A Study on False Belief Tasks. In: Blackburn, P., Lorini, E., Guo, M. (eds) Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science(), vol 11813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60292-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-60292-8_22

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-60291-1

  • Online ISBN: 978-3-662-60292-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation