Thinking in Schemas: Robust Syllogistic Reasoning in LLMs

LLMs often mistake what sounds true for what is formally valid. This limitation is especially evident in syllogistic reasoning, where plausible arguments can lead models to endorse conclusions that are logically invalid, a phenomenon known as content effect (CE). We present Boethius, a schema-guided framework for syllogistic reasoning that disentangles semantic plausibility from logical validity. Boethius adopts an auditable, quasi-formal reasoning process with two complementary stages: a Schema Module, which deduces the underlying logical form by analysing the formal structure of the premises, and an Instantiation Module, which instantiates this form over the concrete argument and evaluates validity independently of content-level semantics. Our results show that Boethius consistently outperforms existing approaches, improving syllogistic reasoning accuracy while substantially reducing CE. These gains hold for both large models in a pure in-context learning setting and smaller models trained via schema-guided trajectories using supervised fine-tuning and optimisation-based refinement. "Some winged animals are not chickadees. It is certain that all chickadees are birds. Therefore, some winged animals are not birds." SCHEMA MODULE INSTANTIATION MODULE PREMISES IDENTIFICATION: P1: Some winged animals are not chickadees.