Lazy model expansion by incremental grounding BROES DE CAT and MARC DENECKER

Model expansion is a widely accepted way to solve a range of problems. It is achieved by encoding the problem in a declarative (logic) language such that structures which satisfy the specification are solutions to the problem. Model expansion is researched in domains like Knowledge Representation and Answer Set Programming. The ground-andsolve methodology tackles model expansion by converting the predicate descriptions of the problem together with the problem instance data to propositional clauses and afterwards applying a model generator for propositional logic. Ground-and-solve is currently a state-of-the-art approach to model expansion, but a weakness of the approach is that the grounding step is only applicable when the problem instance is finite, and even then the grounding can be exponentially larger than the original description. In this paper we describe a lazy approach to grounding of problems specified in first-order logic that can cope with large and infinite problem domains. It interleaves grounding and propositional model expansion, and by keeping track whether models found for a subset of the full grounding solve the problem, it can forgo determining all propositions in the grounding. The approach is hence both more widely applicable and more efficient for problems where the grounding is large.