We present an algorithm to impute missing values from given data alone, and analyse its performance. The proposed procedure is based on non-numeric rule based data analysis, and aims to maximise consistency of imputation from known values. In contrast to the prevailing statistical imputation algorithms, it does not make representational assumptions or presupposes other model constraints. Therefore, it is suitable for a wide variety of data-sets, and can be used as a pre-processing step before resorting to harder numerical methods.

We extend the theory of knowledge structures by taking into account information about the skills a subject has. In the first part of the paper we exhibit some structural properties of the skill-problem relationship and consequences for the interpretation of concurrent theories in terms of the skill theory. The second part of the paper offers a test theory based on skill functions: We present measurements for the data consistency of the skill-problem relationship, and estimate abilities in terms of lower and/or upper boundaries of problem states and skills, given a special instance of the skill-problem relationship. Some practical considerations are discussed, which enable the user of a skill based system to optimise a partial theory about the skill based behaviour of subjects based on empirical results.