ProofSketcher: Hybrid LLM + Lightweight Proof Checker for Reliable Math/Logic Reasoning
This addresses the challenge of ensuring reliable reasoning in mathematical and logical domains for users of LLMs, though it is an incremental improvement over existing interactive theorem provers.
The paper tackles the problem of LLMs producing mathematically or logically flawed arguments that are hard to detect, by introducing a hybrid pipeline where an LLM generates a typed proof sketch and a lightweight trusted kernel expands it into explicit proof obligations, resulting in improved reliability without requiring full formalization.
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference patterns, or appeals to a lemma that cannot be derived logically out of the context being discussed. These omissions are infamously hard to notice solely out of the text, as even the misconstrued construction still may seem mostly accurate. Conversely, interactive theorem provers like Lean and Coq have rigorous reliability by ensuring that syntactic and semantic statements only accept statements that can pass all the syntactic and semantic steps in the program which is a small trusted kernel of the language type-checks with. Despite the fact that this technique provides strong guarantees, it comes at quite a heavy price: the evidence must be completely formalized, and the evidence user or a auxiliary search program must provide an avalanche of low-level information. This paper presents a hybrid pipeline where an LLM generates a typed proof sketch in a compact DSL and a lightweight trusted kernel expands the sketch into explicit proof obligations.