Three-way logical question answering (QA) assigns one of $\text{True}$, $\text{False}$, or $\text{Unknown}$ to a hypothesis $H$ given a premise set $S$. We study this task as a compact compositional inference problem: predictions for $H$ and for a mechanically negated hypothesis $\neg H$ should agree under a deterministic negation map. Despite this simple structure, large language models (LLMs) can exhibit two practical failure modes: (i) negation inconsistency, where answers to $H$ and $\neg H$ violate the required label mapping, and (ii) epistemic $\text{Unknown}$, where the model abstains even when one side is entailed. We introduce CGD-PD, a lightweight, training-free test-time layer that combines neural 3-way classification, symbolic negation-consistency projection, and targeted binary entailment probes. On one validation split of FOLIO's first-order logic fields, CGD-PD improves accuracy by 4.4 points on GPT-5.2 and 6.8 points on Claude Sonnet 4.5, while reducing $\text{Unknown}$ predictions and epistemic abstention. These results provide a controlled proof of concept that simple logical composition at inference time can help evaluate and improve LLM reasoning reliability; they do not, by themselves, establish robustness beyond this formal benchmark setting.

翻译：三值逻辑问答（QA）针对前提集 $S$ 中的假设 $H$ 分配 $\text{True}$（真）、$\text{False}$（假）或 $\text{Unknown}$（未知）之一。我们将该任务视为一个紧凑的组合推理问题：在确定性否定映射下，对 $H$ 的预测与对机械否定假设 $\neg H$ 的预测应保持一致。尽管结构简单，大型语言模型（LLM）仍可能表现出两种实际故障模式：（i）否定不一致性，即对 $H$ 和 $\neg H$ 的答案违反标签映射要求；（ii）认知上的 $\text{Unknown}$，即模型在某一侧蕴含成立时仍选择弃权。我们提出 CGD-PD，一种轻量级、无需训练的测试时层，它结合了神经三值分类、符号否定一致性投影以及针对性二值蕴涵探测。在 FOLIO 一阶逻辑字段的一个验证子集上，CGD-PD 在 GPT-5.2 上提升准确率 4.4 个百分点，在 Claude Sonnet 4.5 上提升 6.8 个百分点，同时减少了 $\text{Unknown}$ 预测和认知弃权。这些结果提供了一个受控的概念验证，表明推理时的简单逻辑组合有助于评估和提升 LLM 推理可靠性；但本身并不足以证明在此形式基准环境之外的鲁棒性。