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

Journal of Logic, Language and Information 22 (3):297-314 (2013)
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Abstract

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

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Citations of this work

Hybrid-Logical Reasoning in the Smarties and Sally-Anne Tasks.Torben Braüner - 2014 - Journal of Logic, Language and Information 23 (4):415-439.

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References found in this work

First-Order Logic.Raymond Merrill Smullyan - 1968 - Berlin, Germany: New York [Etc.]Springer-Verlag.
Minimal Rationality.Christopher Cherniak - 1988 - Behaviorism 16 (1):89-92.
First-order Logic.William Craig - 1975 - Journal of Symbolic Logic 40 (2):237-238.

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