Predictive Theory of Mind Models Based on Public Announcement Logic

Jakob Dirk Top*, Catholijn Jonker, Rineke Verbrugge, Harmen de Weerd

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


Epistemic logic can be used to reason about statements such as ‘I know that you know that I know that φ ’. In this logic, and its extensions, it is commonly assumed that agents can reason about epistemic statements of arbitrary nesting depth. In contrast, empirical findings on Theory of Mind, the ability to (recursively) reason about mental states of others, show that human recursive reasoning capability has an upper bound. In the present paper we work towards resolving this disparity by proposing some elements of a logic of bounded Theory of Mind, built on Public Announcement Logic. Using this logic, and a statistical method called Random-Effects Bayesian Model Selection, we estimate the distribution of Theory of Mind levels in the participant population of a previous behavioral experiment. Despite not modeling stochastic behavior, we find that approximately three-quarters of participants’ decisions can be described using Theory of Mind. In contrast to previous empirical research, our models estimate the majority of participants to be second-order Theory of Mind users.

Original languageEnglish
Title of host publicationDynamic Logic. New Trends and Applications - 5th International Workshop, DaLi 2023, Revised Selected Papers
EditorsNina Gierasimczuk, Fernando R. Velázquez-Quesada
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages19
ISBN (Print)9783031517761
Publication statusPublished - 13-Jan-2024
Event5th International Workshop on Dynamic Logic - New Trends and Applications, DaLi 2023 - Tbilisi, Georgia
Duration: 15-Sept-202316-Sept-2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14401 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference5th International Workshop on Dynamic Logic - New Trends and Applications, DaLi 2023


  • Behavioral Modeling
  • Cognitive Science
  • Epistemic Logic
  • Public Announcement Logic
  • Random-Effects Bayesian Model Selection
  • Theory of Mind

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