Construction of Knowledge Spaces for Problem Solving in Chess
An extension of the theory of knowledge spaces introduced by Doignon and Falmagne (1985) is presented. This extension allows surmise relations and quasi-ordinal knowledge spaces to be constructed with the help of the formal principles ‘set inclusion’2 and ‘sequence inclusion’ from basic units of knowledge. The basic units for constructing the surmise relation in chess are the tactical elements of the game — the ‘motives’. In terms of problem solving, these motives can be regarded as subgoals in the process of problem solving. Two experimental investigations of chess knowledge test the empirical validity of the two principles and show that the theory of knowledge spaces is suitable for testing psychological models.
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