Rulebreakers Challenge: Revealing a Blind Spot in Large Language Models' Reasoning with Formal Logic

Formal logic has long been applied to natural language reasoning, but this approach can sometimes lead to conclusions that, while logically entailed, are factually inconsistent with the premises or are not typically inferred by humans. This study introduces the concept of "rulebreakers", which refers to instances where logical entailment diverges from factually acceptable inference. We present RULEBREAKERS, a novel dataset for evaluating Large Language Models' (LLMs) ability to distinguish between rulebreakers and non-rulebreakers. Focusing on modus tollens and disjunctive syllogism, we assess six state-of-the-art LLMs using RULEBREAKERS, measuring their performance in terms of token-level exact accuracy and model confidence. Our findings reveal that while most models perform poorly to moderately in recognizing rulebreakers, they demonstrate a latent ability to distinguish rulebreakers when assessed by their confidence levels. Further analysis suggests that the failure to recognize rulebreakers is potentially associated with the models' world knowledge and their attention distribution patterns. This research highlights the limitation of LLMs' reasoning capabilities, and contributes to the ongoing discussion on reasoning in LLMs.