Lifted Unit Propagation for Effective Grounding

Abstract

A grounding of a formula $\phi$ over a given finite domain is a ground formula which is equivalent to $\phi$ on that domain. Very effective propositional solvers have made grounding-based methods for problem solving increasingly important, however for realistic problem domains and instances, the size of groundings is often problematic. A key technique in ground (e.g., SAT) solvers is unit propagation, which often significantly reduces ground formula size even before search begins. We define a "lifted" version of unit propagation which may be carried out prior to grounding, and describe integration of the resulting technique into grounding algorithms. We describe an implementation of the method in a bottom-up grounder, and an experimental study of its performance.