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.

An increasing amount of research in Natural Language Inference (NLI) focuses on the application and evaluation of Large Language Models (LLMs) and their reasoning capabilities. Despite their success, however, LLMs are still prone to factual errors and inconsistencies in their explanations, offering limited control and interpretability for inference in complex domains. In this paper, we focus on ethical NLI, investigating how hybrid neuro-symbolic techniques can enhance the logical validity and alignment of ethical explanations produced by LLMs. Specifically, we present an abductive-deductive framework named Logic-Explainer, which integrates LLMs with an external backward-chaining solver to refine step-wise natural language explanations and jointly verify their correctness, reduce incompleteness and minimise redundancy. An extensive empirical analysis demonstrates that Logic-Explainer can improve explanations generated via in-context learning methods and Chain-of-Thought (CoT) on challenging ethical NLI tasks, while, at the same time, producing formal proofs describing and supporting models’ reasoning. As ethical NLI requires commonsense reasoning to identify underlying moral violations, our results suggest the effectiveness of neuro-symbolic methods for multi-step NLI more broadly, opening new opportunities to enhance the logical consistency, reliability, and alignment of LLMs.

Natural language explanations represent a proxy for evaluating explanation-based and multi-step Natural Language Inference (NLI) models. However, assessing the validity of explanations for NLI is challenging as it typically involves the crowd-sourcing of apposite datasets, a process that is time-consuming and prone to logical errors. To address existing limitations, this paper investigates the verification and refinement of natural language explanations through the integration of Large Language Models (LLMs) and Theorem Provers (TPs). Specifically, we present a neuro-symbolic framework, named Explanation-Refiner, that integrates TPs with LLMs to generate and formalise explanatory sentences and suggest potential inference strategies for NLI. In turn, the TP is employed to provide formal guarantees on the logical validity of the explanations and to generate feedback for subsequent improvements. We demonstrate how Explanation-Refiner can be jointly used to evaluate explanatory reasoning, autoformalisation, and error correction mechanisms of state-of-the-art LLMs as well as to automatically enhance the quality of explanations of variable complexity in different domains.