Computational representations of herbrand models using grammars

Abstract

Finding computationally valuable representations of models of predicate logic formulas is an important subtask in many fields related to automated theorem proving, e.g. automated model building or semantic resolution. In this article we investigate the use of context-free languages for representing single Herbrand models, which appear to be a natural extension of ``linear atomic representations'' already known from the literature. We focus on their expressive power (which we find out to be exactly the finite models) and on algorithmic issues like clause evaluation and equivalence test (which we solve by using a resolution theorem prover), thus proving our approach to be an interesting base for investigating connections between formal language theory and automated theorem proving and model building.