We extend the theory of Boolean functions, especially in respect to representing these functions in the disjunctive or conjunctive normal forms, onto the case of finite predicates. So, we show that it is useful to apply the language of Boolean vectors and matrices, developing efficient methods for calculation over finite predicates. This means that finite predicates should be decomposed into some binary units, which will correspond to components of Boolean vectors and matrices and should be represented as combinations of these units. Further, we define probabilities in data bases using Boolean matrices representing finite predicates. We also show that it is natural to try and present knowledge in the most compact form, which allows reducing the time of inference, by which the recognition problems are solved.