Consistency-Guided Decoding with Proof-Driven Disambiguation for Three-Way Logical Question Answering

Abstract: Three-way logical question answering (QA) assigns $True/False/Unknown$ to a hypothesis $H$ given a premise set $S$. While modern LLMs can be accurate on isolated examples, we identify two recurring failure modes in 3-way logic QA: (i) negation inconsistency, where answers to $H$ and $\neg H$ violate the deterministic label mapping, and (ii) epistemic $Unknown$, where the model predicts $Unknown$ due to uncertainty or instability even when $S$ entails one side. We present CGD-PD, a lightweight test-time layer that (a) queries a single 3-way classifier on both $H$ and a mechanically negated form of $H$, (b) projects the pair onto a negation-consistent decision when possible, and (c) invokes a proof-driven disambiguation step that uses targeted binary entailment probes to selectively resolve $Unknown$ outcomes, requiring only an average of 4-5 model calls. On the FOLIO benchmark's first-order-logic fields, CGD-PD yields consistent gains across frontier LLMs, with relative improvements in accuracy of up to 16% over the base model, while also reducing $Unknown$ predictions.