Functional Dependencies in Horn Theories

This paper studies functional dependencies in Horn theories, both when the theory is represented by its clausal form and when it is deened as the Horn envelope of a set of models. We provide polynomial algorithms for the recognition of whether a given functional dependency holds in a given Horn theory, as well as polynomial algorithms for the generation of some representative sets of functional dependencies that hold in a given Horn theory. We show that some functional dependencies inference problems are computationally diicult. We also study the structure of functional dependencies that hold in a Horn theory, show that every such functional dependency is in fact a single positive term Boolean function, and prove that for any Horn theory its set of functional dependencies is quasi-acyclic. Finally, we consider the problem of condensing a Horn theory, prove that any Horn theory has a unique condensation, and develope eecient polynomial algorithms for condensing Horn theories.