On LLM-generated Logic Programs and their Inference Execution Methods

Abstract: LLMs trained on petabytes of data are highly compressed repositories of a significant proportion of the knowledge accumulated and distilled so far. In this paper we study techniques to elicit this knowledge in the form of several classes of logic programs, including propositional Horn clauses, Dual Horn clauses, relational triplets and Definite Clause Grammars. Exposing this knowledge as logic programs enables sound reasoning methods that can verify alignment of LLM outputs to their intended uses and extend their inference capabilities. We study new execution methods for the generated programs, including soft-unification of abducible facts against LLM-generated content stored in a vector database as well as GPU-based acceleration of minimal model computation that supports inference with large LLM-generated programs.