Journal of Logic, Language and Information

, Volume 22, Issue 3, pp 297–314 | Cite as

An Analytic Tableaux Model for Deductive Mastermind Empirically Tested with a Massively Used Online Learning System

  • Nina GierasimczukEmail author
  • Han L. J. van der Maas
  • Maartje E. J. Raijmakers


The paper is concerned with the psychological relevance of a logical model for deductive reasoning. We propose a new way to analyze logical reasoning in a deductive version of the Mastermind game implemented within a popular Dutch online educational learning system (Math Garden). Our main goal is to derive predictions about the difficulty of Deductive Mastermind tasks. By means of a logical analysis we derive the number of steps needed for solving these tasks (a proxy for working memory load). Our model is based on the analytic tableaux method, known from proof theory. We associate the difficulty of Deductive Mastermind game-items with the size of the corresponding logical trees obtained by the tableaux method. We derive empirical hypotheses from this model. A large group of students (over 37 thousand children, 5–12 years of age) played the Deductive Mastermind game, which gave empirical difficulty ratings of all 321 game-items. The results show that our logical approach predicts these item ratings well, which supports the psychological relevance of our model.


Deductive Mastermind Mastermind game Deductive reasoning Analytic tableaux Math Garden (Rekentuin) Educational tools 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Nina Gierasimczuk
    • 1
    Email author
  • Han L. J. van der Maas
    • 2
  • Maartje E. J. Raijmakers
    • 2
  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of PsychologyUniversity of AmsterdamAmsterdamThe Netherlands

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