# Conflict-Aware Fusion: Mitigating Logic Inertia in Large Language Models via Structured Cognitive Priors

arXiv: https://arxiv.org/abs/2512.06393 · HTML: https://mlsanity.com/paper/2512.06393/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 52 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 30 of 39)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Deliberative Alignment: Reasoning Enables Safer Language Models](https://mlsanity.com/paper/2412.16339/) (2024)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [ARES: An Automated Evaluation Framework for Retrieval-Augmented Generation Systems](https://mlsanity.com/paper/2311.09476/) (2023)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Logic-Guided Data Augmentation and Regularization for Consistent Question Answering](https://mlsanity.com/paper/2004.10157/) (2020)
- [A Logic-Driven Framework for Consistency of Neural Models](https://mlsanity.com/paper/1909.00126/) (2019)
- [Large Language Models Are Not Strong Abstract Reasoners](https://mlsanity.com/paper/2305.19555/) (2023)
- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Text](https://mlsanity.com/paper/2105.03659/) (2021)
- [Benchmarks for Automated Commonsense Reasoning: A Survey](https://mlsanity.com/paper/2302.04752/) (2023)
- [Leanabell-Prover-V2: Verifier-integrated Reasoning for Formal Theorem Proving via Reinforcement Learning](https://mlsanity.com/paper/2507.08649/) (2025)
- [Deliberate Reasoning in Language Models as Structure-Aware Planning with an Accurate World Model](https://mlsanity.com/paper/2410.03136/) (2024)
- [AbductionRules: Training Transformers to Explain Unexpected Inputs](https://mlsanity.com/paper/2203.12186/) (2022)
- [Multi-Step Deductive Reasoning Over Natural Language: An Empirical Study on Out-of-Distribution Generalisation](https://mlsanity.com/paper/2207.14000/) (2022)
- [Don't Let It Hallucinate: Premise Verification via Retrieval-Augmented Logical Reasoning](https://mlsanity.com/paper/2504.06438/) (2025)
- [CodeCrash: Exposing LLM Fragility to Misleading Natural Language in Code Reasoning](https://mlsanity.com/paper/2504.14119/) (2025)
- [Mathematics, word problems, common sense, and artificial intelligence](https://mlsanity.com/paper/2301.09723/) (2023)
- [Abstract Meaning Representation-Based Logic-Driven Data Augmentation for Logical Reasoning](https://mlsanity.com/paper/2305.12599/) (2023)

## Built on by (most cited first, 5 of 5)

- [DIVE: Unlocking Self-Improvement in Frozen Language Models Through Diversity-Driven Skill Evolution](https://mlsanity.com/paper/2608.12486/) (2026)
- [SciTrue: Reliable Scientific Claim Validation with Frontier and Open Language Models at the NTCIR SciClaimEval Task](https://mlsanity.com/paper/2609.00654/) (2026)
- [Nous: An Attempt to Extract and Inject the Cognition Behind Prediction-Market Behavior](https://mlsanity.com/paper/2606.13038/) (2026)
- [Beyond Surface Forms: Symbolic Edits as a Test for Logical Reasoning with LLMs](https://mlsanity.com/paper/2608.30256/) (2026)
- [Can Language Models Learn to Reject Their Own Bad Reasoning Steps?](https://mlsanity.com/paper/2610.05976/) (2026)

## Abstract (arXiv)

Large language models (LLMs) achieve high accuracy on many reasoning benchmarks but remain brittle under structural perturbations of rule-based systems. We introduce a diagnostic framework with four stress tests -- redundant vs. essential rule deletion, contradictory-rule injection, logic-preserving rewrites, and multi-law stacking -- and use it to expose Logic Inertia: the tendency of generative LLMs (Qwen2/3, TinyLlama, GPT-4o, Gemma-3-4B-IT) and the encoder-only BERT baseline to persist along learned deductive trajectories under inconsistent premises. The collapse is sharp: untreated baselines fall from accuracy 1.00 on the base task to 0.00 on contradiction injection (instance-level exact match), and GPT-4o resolves only 56.0% of contradiction cases. We propose Conflict-Aware Fusion, a four-stage training pipeline that enforces verification-before-deduction as a learned structural prior: (i) SFT establishes the verification preamble; (ii) DPO sharpens the halt-on-contradiction decision boundary; (iii) Logical Invariance REgularisation (LIRE) penalises divergence between logically equivalent rule formulations via symmetric KL; (iv) Reinforcement Learning from Verification Feedback (RLVF) uses a symbolic forward-chaining engine as a deterministic oracle reward, jointly optimising invariance and sensitivity. The pipeline saturates all four primary stress tests for both 1.5B and 8B backbones. We further validate a Phase 2 extension that replaces the propositional oracle with a Lean 4 kernel, attaining 99.0% kernel agreement on the 105 classically-derivable (T) questions within a stratified 187-question Lean-translated sample (overall 71.7% across both polarities), providing a sound upgrade path to formally verified RL training. Code and benchmark: https://github.com/14H034160212/lemo