Component-based Construction of Surmise Relations for Chess Problems

An approach to construct surmise relations or quasi-ordinal knowledge spaces through ordering principles is described. The ordering principles apply to the components of problems, which are considered as the basic units of knowledge necessary to solve the problems properly. We describe the three ordering principles “set inclusion”, “multiset inclusion” and “sequence inclusion” and an application of these principles to the construction of surmise relations on sets of chess problems. The basic units for the construction of surmise relations 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. The em-pirical validity of the described ordering principles is tested in two experimental investigations. The results show that the two principles “multiset inclusion” and “sequence inclusion” predict the difficulty of chess problems rather well, whereas the principle “set inclusion” is clearly insufficient in this field. The experimental investigations also demonstrate the suitability of the theory of knowledge spaces for testing psychological theories.