Skills and knowledge structures†

Abstract

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 function assigns to each set X of skills the set of problems which can be solved with these skills (a knowledge state) . We explore the natural properties of such functions and show that these concepts are basically 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 (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, and discuss various ways to supply a set of knowledge states with an underlying skill theory. Finally, a procedure is described to determine a skill function using coverings in partial orders which is applied to set A of the Coloured Progressive Matrices test (Raven, 1965).