Are LLMs Reliable Translators of Logical Reasoning Across Lexically Diversified Contexts?

Neuro-symbolic approaches combining large language models (LLMs) with solvers excels in logical reasoning problems need long reasoning chains. In this paradigm, LLMs serve as translators, converting natural language reasoning problems into formal logic formulas. Then reliable symbolic solvers return correct solutions. Despite their success, we find that LLMs, as translators, struggle to handle lexical diversification, a common linguistic phenomenon, indicating that LLMs as logic translators are unreliable in real-world scenarios. Moreover, existing logical reasoning benchmarks lack lexical diversity, failing to challenge LLMs' ability to translate such text and thus obscuring this issue. In this work, we propose SCALe, a benchmark designed to address this significant gap through **logic-invariant lexical diversification**. By using LLMs to transform original benchmark datasets into lexically diversified but logically equivalent versions, we evaluate LLMs' ability to consistently map diverse expressions to uniform logical symbols on these new datasets. Experiments using SCALe further confirm that current LLMs exhibit deficiencies in this capability. Building directly on the deficiencies identified through our benchmark, we propose a new method, MenTaL, to address this limitation. This method guides LLMs to first construct a table unifying diverse expressions before performing translation. Applying MenTaL through in-context learning and supervised fine-tuning (SFT) significantly improves the performance of LLM translators on lexically diversified text. Our code is now available at https://github.com/wufeiwuwoshihua/LexicalDiver.

Leveraging LLMs for Hypothetical Deduction in Logical Inference: A Neuro-Symbolic Approach

Large Language Models (LLMs) have exhibited remarkable potential across a wide array of reasoning tasks, including logical reasoning. Although massive efforts have been made to empower the logical reasoning ability of LLMs via external logical symbolic solvers, crucial challenges of the poor generalization ability to questions with different features and inevitable question information loss of symbolic solver-driven approaches remain unresolved. To mitigate these issues, we introduce LINA, a LLM-driven neuro-symbolic approach for faithful logical reasoning. By enabling an LLM to autonomously perform the transition from propositional logic extraction to sophisticated logical reasoning, LINA not only bolsters the resilience of the reasoning process but also eliminates the dependency on external solvers. Additionally, through its adoption of a hypothetical-deductive reasoning paradigm, LINA effectively circumvents the expansive search space challenge that plagues traditional forward reasoning methods. Empirical evaluations demonstrate that LINA substantially outperforms both established propositional logic frameworks and conventional prompting techniques across a spectrum of five logical reasoning tasks. Specifically, LINA achieves an improvement of 24.34% over LINC on the FOLIO dataset, while also surpassing prompting strategies like CoT and CoT-SC by up to 24.02%. Our code is available at https://github.com/wufeiwuwoshihua/nshy.