Aligning with Logic: Measuring, Evaluating and Improving Logical Consistency in Large Language Models

Recent research in Large Language Models (LLMs) has shown promising progress related to LLM alignment with human preferences. LLM-empowered decision-making systems are expected to be predictable, reliable and trustworthy, which implies being free from paradoxes or contradictions that could undermine their credibility and validity. However, LLMs still exhibit inconsistent and biased behaviour when making decisions or judgements. In this work, we focus on studying logical consistency of LLMs as a prerequisite for more reliable and trustworthy systems. Logical consistency ensures that decisions are based on a stable and coherent understanding of the problem, reducing the risk of erratic or contradictory outputs. We first propose a universal framework to quantify the logical consistency via three fundamental proxies: transitivity, commutativity and negation invariance. We then evaluate logical consistency, using the defined measures, of a wide range of LLMs, demonstrating that it can serve as a strong proxy for overall robustness. Additionally, we introduce a data refinement and augmentation technique that enhances the logical consistency of LLMs without sacrificing alignment to human preferences. It augments noisy and sparse pairwise-comparison annotations by estimating a partially or totally ordered preference rankings using rank aggregation methods. Finally, we show that logical consistency impacts the performance of LLM-based logic-dependent algorithms, where LLMs serve as logical operators.