The Expanded Implication Problem of

The implication problem is the problem of deciding whether a given set of dependencies entails other dependencies. Up to now, the entailment of excluded dependencies or independencies is only regarded on a metalogical level, which is not suitable for an automatic inference process. But, the inference of independencies is of great importance for new topics in database research like knowledge discovery in databases. In this paper, the expanded implication problem is discussed in order to decide entailment of dependencies and independencies. The main results are axiomatizations of functional, inclusion and multivalued independencies and the corresponding inference relations. Also, we discuss the use of independencies in knowledge discovery in databases and semantic query optimization.