Model Generation for Horn Logic with Stratified Negation

Model generation is an important formal technique for finding interesting instances of computationally hard problems. In this paper we study model generation over Horn logic under the closed world assumption extended with stratified negation. We provide a novel three-stage algorithm that solves this problem: First, we reduce the relevant Horn clauses to a set of non-monotonic predicates. Second, we apply a fixed-point procedure to these predicates that reveals candidate solutions to the model generation problem. Third, we encode these candidates into a satisfiability problem that is evaluated with a state-of-the-art SMT solver. Our algorithm is implemented, and has been successfully applied to key problems arising in model-based design.