On LLM-generated Logic Programs and their Inference Execution Methods

2025-02-11

Electronic Proceedings in Theoretical Computer Science

AI Summary

This paper addresses the challenge of implicit and unverifiable knowledge in large language models (LLMs) by introducing a novel paradigm that structurally encodes LLM outputs as executable logical programs—specifically, propositional Horn clauses, dual Horn clauses, relational triples, and definite clause grammars—to enable sound, verifiable reasoning. Methodologically: (1) it designs a soft unification mechanism to semantically align logical facts with LLM-derived vector representations in embedding databases; (2) it proposes a GPU-accelerated minimal model solving algorithm for efficient, scalable inference over large-scale logical programs. Contributions include: the first end-to-end, verifiable extraction of LLM knowledge into multiple formal logical representations; significant improvements in both the scale and speed of logically sound inference; and empirical validation of enhanced knowledge consistency checking and reasoning capability.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Large Language Models (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.

Problem

• Extract logic programs from LLMs
• Verify LLM output alignment
• Accelerate inference execution methods

Innovation

• Generates logic programs from LLM knowledge
• Uses soft-unification for abducible facts
• Accelerates inference with GPU computation