Skills and knowledge structures

Title:	Skills and knowledge structures
Author:	Ivo Düntsch , Dept of Computer Science , Brock University , St Catherines, Ontario, L2S 3A1, Canada Günther Gediga , Institut für Evaluation und Marktanalysen, Brinkstr. 19; D-49143 Jeggen; Germany (Equal authorship implied)
Status:	British Journal of Mathematical and Statistical Psychology 48 (1995), 9 - 27
Abstract:	Suppose that Q is a set of problems and S is a set of skills. A skill function assigns to each problem q in Q those sets of skills which are minimally sufficient to solve q; a problem function assigns to each set X of skills the set of problems which can be solved with these skills. We explore the natural properties of such functions and show that these concepts are basically the same. Furthermore, we show that given any family K of subsets of Q which includes the empty set and Q, there is a set S of (abstract) skills and a problem function whose range is just K. We also give a bound for the number of skills needed to generate a specific set of knowledge states: If card(K) = m + 2 > 6, such an S can be chosen with no more than log(m) + log(log(m)) + 2 elements. Finally, a procedure is described to determine the skill function using coverings in partial orders which is applied to set A of Raven's Coloured Progressive Matrices test.