The implication problem for data dependencies

Abstract

In this paper we study the implication and the finite implication problems for data dependencies. When all dependencies are total the problems are equivalent and solvable but are NP-hard, i.e., probably computationally intractable. For non-total dependencies the implication problem is unsolvable, and the finite implication problem is not even partially solvable. Thus, there can be no formal system for finite implication. The meta decision problems of deciding for a given class of dependencies whether the implication problem is solvable or whether implication is equivalent to finite implication are also unsolvable.