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

arXiv: https://arxiv.org/abs/2604.06196 · HTML: https://mlsanity.com/paper/2604.06196/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models](https://mlsanity.com/paper/2109.05093/) (2021)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Measuring Compositional Generalization: A Comprehensive Method on Realistic Data](https://mlsanity.com/paper/1912.09713/) (2019)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [Lexically Constrained Decoding for Sequence Generation Using Grid Beam Search](https://mlsanity.com/paper/1704.07138/) (2017)
- [Fast Lexically Constrained Decoding with Dynamic Beam Allocation for Neural Machine Translation](https://mlsanity.com/paper/1804.06609/) (2018)
- [P-FOLIO: Evaluating and Improving Logical Reasoning with Abundant Human-Written Reasoning Chains](https://mlsanity.com/paper/2410.09207/) (2024)
- [Metamorphic Testing of Large Language Models for Natural Language Processing](https://mlsanity.com/paper/2511.02108/) (2025)

## Abstract (arXiv)

Three-way logical question answering (QA) assigns one of True, False, or 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 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 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.