# Compositional Consistency-Guided Decoding for Three-Way Logical Question Answering

Source: [Compositional Consistency-Guided Decoding for Three-Way Logical Question Answering](<https://www.sota2.com/research/paper/69d732627d0172140ec76958>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-29T05:00:05.519Z

Authors: Tianyi Huang, Ming Hou, Jiaheng Su, Yutong Zhang, Ziling Zhang

Published: 2026-03-12T18:26:16.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Logical Reasoning on FOLIO FOL fields (val)](<https://www.sota2.com/research/sota/logical-reasoning-on-folio-fol-fields-val.md>): Logical reasoning; FOLIO FOL fields (val); Accuracy: 68.1.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2604.06196>)

[PDF](<https://arxiv.org/pdf/2604.06196.pdf>)