SKILLS AND KNOWLEDGE STRUCTURES

Suppose that Q is a set of problems and S is a set of skills. A skill function assigns to each problem q - i.e. to each element of Q - those sets of skills which are minimally sufficient to solve q; a problem f unction assigns to each set X of skills the set of problems which can be solved with these skills (a knowledge state). We explore the natura l properties of such functions and show that these concepts are basica lly the same. Furthermore, we show that for every family K of subsets of Q which includes the empty set and Q, there are a set S of (abstrac t) 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 k nowledge states, and discuss various ways to supply a set of knowledge states with an underlying skill theory. Finally, a procedure is descr ibed to determine a skill function using coverings in partial orders w hich is applied to set A of the Coloured Progressive Matrices test (Ra ven, 1965).