Testing the General Deductive Reasoning Capacity of Large Language Models Using OOD Examples

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to compositional proofs. However, they have difficulty generalizing to longer proofs, and they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction. * Equal contribution. †,∆ GPT and PaLM experiments in this paper were conducted independently. Authors affiliated with NYU † were responsible for the GPT experiments, and authors affiliated with Google ∆ were responsible for the PaLM experiments. 37th Conference on Neural Information Processing Systems (NeurIPS 2023).