Logical and psychological analysis of deductive mastermind

The paper proposes a way to analyze logical reasoning in a deductive version of the Mastermind game implemented within the Math Garden educational system. Our main goal is to derive predictions about the cognitive difficulty of game-plays, e.g., the number of steps needed for solving the logical tasks or the working memory load. Our model is based on the analytic tableaux method, known from proof theory. We associate the difficulty of the Deductive Mastermind game-items with the size of the corresponding logical tree derived by the tableau method. We discuss possible empirical hypotheses based on this model, and preliminary results that prove the relevance of our theory.

[1]  Jakub Szymanik,et al.  Quantifiers in TIME and SPACE : computational complexity of generalized quantifiers in natural language , 2009 .

[2]  Eric Sven Ristad.  The language complexity game , 1993 .

[3]  Jakub Szymanik,et al.  A computational approach to quantifiers as an explanation for some language impairments in schizophrenia. , 2011, Journal of communication disorders.

[4]  Jakub Szymanik,et al.  Computational complexity of polyadic lifts of generalized quantifiers in natural language , 2010 .

[5]  K. Koyama,et al.  An Optimal Mastermind Strategy , 1993 .

[6]  Barteld P. Kooi.  Yet Another Mastermind Strategy , 2005, J. Int. Comput. Games Assoc..

[7]  Guo-Qiang Zhang,et al.  Mastermind is NP-Complete , 2005, ArXiv.

[8]  Nina Gierasimczuk,et al.  Branching Quantification v. Two-way Quantification , 2009, J. Semant..

[9]  Rineke Verbrugge,et al.  Learning to Apply Theory of Mind , 2008, J. Log. Lang. Inf..

[10]  Vasek Chvátal,et al.  Mastermind , 1983, Comb..

[11]  S. Klinkenberg,et al.  Rekentuin.nl: combinatie van oefenen en toetsen , 2010 .

[12]  Iris van Rooij,et al.  The Tractable Cognition Thesis , 2008, Cogn. Sci..

[13]  Jakub Szymanik,et al.  Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational Model , 2010, Cogn. Sci..

[14]  S. Klinkenberg,et al.  Computer adaptive practice of Maths ability using a new item response model for on the fly ability and difficulty estimation , 2011, Comput. Educ..

[15]  Evert W. Beth,et al.  Semantic Entailment And Formal Derivability , 1955 .

[16]  D. Knuth.  The Computer as Master Mind , 1977 .

[17]  A. Elo.  The rating of chessplayers, past and present , 1978 .

[18]  Rineke Verbrugge,et al.  Logic Meets Cognition: Empirical Reasoning in Games , 2010, MALLOW.

[19]  Johan Kwisthout,et al.  Intentional Communication: Computationally Easy or Difficult? , 2011, Front. Hum. Neurosci..

[20]  Sujata Ghosh,et al.  On combining cognitive and formal modeling: A case study involving strategic reasoning , 2011 .