First-Order Automatic Literal Model Generation

Abstract

Given a finite consistent set of ground literals, we present an algorithm that generates a complete first-order logic interpretation, i.e., an interpretation for all ground literals over the signature and not just those in the input set, that is also a model for the input set. The interpretation is represented by first-order linear literals. It can be effectively used to evaluate clauses. A particular application are SCL stuck states. The SCL (Simple Clause Learning) calculus always computes with respect to a finite number of ground literals. It then finds either a contradiction or a stuck state being a model with respect to the considered ground literals. Our algorithm builds a complete literal interpretation out of such a stuck state model that can then be used to evaluate the clause set. If all clauses are satisfied an overall model has been found. If it does not satisfy some clause, this information can be effectively explored to extend the scope of ground literals considered by SCL.