Faithful and Robust LLM-Driven Theorem Proving for NLI Explanations

TL;DR

This paper proposes strategies to enhance the faithfulness and robustness of large language models in formal theorem proving for natural language inference explanations, significantly improving accuracy and efficiency.

Contribution

It introduces novel methods to reduce semantic loss, correct syntactic errors, and leverage logical expressions, advancing LLM-TP integration for more reliable NLI explanations.

Findings

Autoformalisation accuracy improved by up to 39.77%

Explanation refinement accuracy increased by up to 51.5%

Hybrid LLM-TP architecture reduces verification iterations

Abstract

Natural language explanations play a fundamental role in Natural Language Inference (NLI) by revealing how premises logically entail hypotheses. Recent work has shown that the interaction of large language models (LLMs) with theorem provers (TPs) can help verify and improve the validity of NLI explanations. However, TPs require translating natural language into machine-verifiable formal representations, a process that introduces the risk of semantic information loss and unfaithful interpretation, an issue compounded by LLMs' challenges in capturing critical logical structures with sufficient precision. Moreover, LLMs are still limited in their capacity for rigorous and robust proof construction within formal verification frameworks. To mitigate issues related to faithfulness and robustness, this paper investigates strategies to (1) alleviate semantic loss during autoformalisation, (2) efficiently identify and correct syntactic errors in logical representations, (3) explicitly use logical expressions to guide LLMs in generating structured proof sketches, and (4) increase LLMs' capacity of interpreting TP's feedback for iterative refinement. Our empirical results on e-SNLI, QASC and WorldTree using different LLMs demonstrate that the proposed strategies yield significant improvements in autoformalisation (+18.46%, +34.2%, +39.77%) and explanation refinement (+29.5%, +51.5%, +41.25%) over the state-of-the-art model. Moreover, we show that specific interventions on the hybrid LLM-TP architecture can substantially improve efficiency, drastically reducing the number of iterations required for successful verification.