Cognitive Complexity of Logical Reasoning in Games: Automated Theorem Proving Perspective
Katrine B. P. Thoft, Nina Gierasimczuk · Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU) · 2019
We use formal proof techniques from artificial intelligence and mathematical logic to analyse human reasoning in problemsolving. We focus on the Deductive Mastermind game, as implemented in the Dutch massive online learning system forchildren, Math Garden. The game is formalised in propositional logic and the game-playing procedure is given a form of alogical proof. We use Resolution and Natural Deduction proof methods (implemented in JAVA). The difficulty of a partic-ular logical reasoning step is associated with the computationally obtained parameters of the proofs, which are comparedwith each other, and against the empirical difficulty of the game. We show, among others, that the complexity parame-ters derived from Natural Deduction agree with the Analytical Tableaux parameters, and with the empirical difficulty asexperienced by human subjects.