Inferring Minimal Functional Dependencies in Horn and q-Horn Theories

In this paper, we study various problems related to the inference of minimal functional dependencies in Horn and q-Horn theories. We show that if a Horn theory is represented by a Horn CNF, then there exists an incrementally polynomial algorithm for inferring all minimal functional dependencies. On the other hand, if a Horn theory is represented as the Horn envelope of a given set of models, then there exists a polynomial total time algorithm for this inference problem if and only if there exists such an algorithm for dualizing a positive CNF. Finally, we generalize our results to the case of q-Horn theories, and show that all the considered problems can be reduced in polynomial time to the corresponding problems for Horn theories.