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

TL;DR

This paper introduces Conflict-Aware Fusion, a training pipeline that enhances large language models' reasoning robustness by enforcing verification before deduction, tested through structured stress tests and formal verification methods.

Contribution

It proposes a novel four-stage training framework that mitigates logic inertia in LLMs, improving their reasoning consistency under structural perturbations.

Findings

The pipeline achieves high accuracy on stress tests for multiple model sizes.

It significantly reduces the collapse of reasoning accuracy under contradictions.

The method enables formal verification with a Lean 4 kernel, reaching 99.0% kernel agreement.

Abstract

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