Global decision problems for relational databases

Database dependencies are first-order sentences describing the semantics of databases. Decision problems concerning dependencies divide into local problem, such as whether a set of dependencies logically implies another dependency, and global problems, such as whether a set of dependencies is redundant. In this paper we investigate global problems, that of recognizing properties of sets of dependencies. The main result is a negative result in the spirit of Adjan-Markov-Rabin result for global properties of finitely presented semigroups and groups. We show that the decision problem for any property which is wellbehaved in a certain sense (specifically, if it is nice, non-trivial and hereditary) is recursively unsolvable.