Logicbreaks: A Framework for Understanding Subversion of Rule-based Inference

We study how to subvert large language models (LLMs) from following prompt-specified rules. We model rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form ``if $P$ and $Q$, then $R$'' for some propositions $P$, $Q$, and $R$. We prove that although LLMs can faithfully follow such rules, maliciously crafted prompts can mislead even idealized, theoretically constructed models. Empirically, we find that the reasoning behavior of LLMs aligns with that of our theoretical constructions, and popular attack algorithms find adversarial prompts with characteristics predicted by our theory. Our logic-based framework provides a novel perspective for mechanistically understanding the behavior of LLMs in rule-based settings such as jailbreak attacks.