Disjunctions of Horn Theories and Their Cores

In this paper, we study issues on disjunctions of propositional Horn theories. In particular, we consider deciding whether a disjunction of Horn theories is Horn, and, if not, computing a Horn core, i.e., a maximal Horn theory included in this disjunction. The problems are investigated for different representations of Horn theories, namely for Horn CNFs and characteristic models. While the problems are shown to be intractable in general, we present polynomial time algorithms for bounded disjunctions in the formula-based case.