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

• URL: http://arxiv.org/abs/2604.06196v1
• Date: Thu, 12 Mar 2026 18:26:16 GMT
• Title: Consistency-Guided Decoding with Proof-Driven Disambiguation for Three-Way Logical Question Answering
• Abstract summary: Three-way logical question answering (QA) assigns $True/False/Unknown$ to a hypothesis $H$ given a premise set $S$.<n>We present CGD-PD, a lightweight test-time layer that queries a single 3-way classifier on both $H$ and a mechanically negated form of $H$.
• Score: 4.878198984786631
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Three-way logical question answering (QA) assigns $True/False/Unknown$ to a hypothesis $H$ given a premise set $S$. While modern large language models (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.

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