Suppose thatQis a set of problems and S is a set of skills. Askill functionassigns to each problemqi.e. to each element of Q — those sets of skills which are minimally sufficient to solveq;aproblem functionassigns to each setXof skills the set of problems which can be solved with these skills (aknowledge state). We explore the natural properties of such functions and show that these concepts are basically the same. Furthermore, we show that for every familyKof subsets ofQwhich includes the empty set andQ, there are a setSof (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