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

1. Problem Statement: Logic Inertia

The paper identifies a critical failure mode in Large Language Models (LLMs) termed Logic Inertia. While LLMs (e.g., BERT, Qwen2, TinyLlama) achieve near-perfect accuracy on standard reasoning tasks, they exhibit a "total breakdown" (0% accuracy) when the structural integrity of the rule system is perturbed.

• The Phenomenon: Logic Inertia is defined as the model's tendency to persist along learned deductive trajectories even when foundational premises are contradictory or missing. The models prioritize "completing the inferential chain" over "verifying the validity of premises."
• The Gap: Existing evaluations conflate linguistic competence with logical robustness. Current benchmarks fail to isolate specific structural failures, such as the inability to detect contradictions or the failure to revise conclusions when essential rules are deleted.
• The Blind Spot: The paper argues that scaling data and model size alone is insufficient. Current training paradigms optimize for pattern completion rather than structural verification, leading to confident but logically invalid outputs in the presence of contradictions.

2. Methodology

The authors propose a comprehensive framework consisting of a diagnostic benchmark and a novel architectural solution.

A. Structural Robustness Benchmark

To diagnose these failures, the authors created a controlled evaluation framework derived from a single canonical rule-based system, applying four specific stress tests:

1. Rule Deletion: Distinguishing between removing redundant rules (should not affect the answer) vs. essential rules (should invalidate the deduction).
2. Contradictory Evidence Injection: Introducing explicit contradictions into the premise set to test if the model halts reasoning or hallucinates a conclusion.
3. Logic-Preserving Rewrites: Testing invariance under equivalence-based reformulations of rules.
4. Multi-Law Equivalence Stacking: Testing compositional robustness under complex rule interactions.

Key Finding: Baseline models achieved 1.0000 accuracy on base tasks but dropped to 0.0000 on contradiction tests, confirming the universality of Logic Inertia.

B. Conflict-Aware Fusion (Fusion-Conflict) Architecture

To mitigate Logic Inertia, the authors introduce Fusion-Conflict, grounded in the Cognitive Structure Hypothesis: Reliable multi-step reasoning requires an explicit structural separation between premise verification and deductive execution.

The architecture enforces a Dual-Process reasoning structure within the Chain-of-Thought (CoT) generation:

• System 2 (Verification): A mandatory "Step 1" where the model explicitly checks for contradictions and premise completeness.
• System 1 (Deduction): Only proceeds if the verification step confirms logical consistency. If a contradiction is found, the model must "Halt" rather than continue.

C. Structure-Aligned Optimization Pipeline

The framework utilizes a two-stage training pipeline to internalize this structural bias:

1. Structural Supervised Fine-Tuning (SFT): Trained on 11,200 instances (canonical, perturbed, and contradictory). All samples enforce a mandatory "Step 1: Verify facts" preamble. This establishes premise checking as a default procedural step.
2. Direct Preference Optimization (DPO): Used to refine the model's behavior. Preference pairs are constructed where the "preferred" response correctly detects a contradiction and halts, while the "rejected" response continues to deduce despite the contradiction. This penalizes "hallucinated" checks and reinforces disciplined termination.

3. Key Contributions

1. Diagnostic Benchmark: A unified framework that disentangles the effects of redundancy, incompleteness, and contradiction, revealing the "Asymmetry of Robustness" (high stability in rewrites vs. total collapse in contradictions).
2. Formalization of Logic Inertia: Identifying and naming the specific failure mode where deductive momentum overrides factual reality, a limitation invisible under conventional benchmarks.
3. Fusion-Conflict Framework: A novel architecture that integrates explicit premise validation into the reasoning trajectory, demonstrating that structural verification discipline is as critical as training data scale.

4. Experimental Results

The experiments were conducted on BERT, Qwen2-1.5B, and TinyLlama-1.1B.

• Baseline Performance: Standard models achieved 1.0000 on base tasks but 0.0000 on contradiction tests (Variant 3), confirming Logic Inertia.
• Fusion-Conflict Performance:
  • Contradiction Handling (Variant 3): Achieved 1.0000 accuracy (perfect detection of contradictions and halting of reasoning).
  • Base Task Performance: Maintained 1.0000 accuracy.
  • Essential Rule Deletion (Variant 2): Achieved 0.735 accuracy, a significant improvement over baselines (which dropped to ~0.25), though slightly lower than base performance, indicating a remaining challenge with missing (vs. contradictory) evidence.
• Ablation Studies:
  • SFT Only (Fusion-LRA): Improved contradiction handling to 0.705 but failed to reach 1.000, suggesting SFT teaches the form of verification but not the discipline to halt.
  • SFT + DPO (Fusion-Conflict): The DPO stage was critical, pushing contradiction accuracy from 0.705 to 1.000 by penalizing "shallow alignment" (hallucinating a successful check).
• Out-of-Distribution Generalization: The model was tested on real-world datasets (LogicNLI and MNLI) without fine-tuning on them.
  • LogicNLI: Improved from 58.5% (Baseline) to 98.2%.
  • MNLI (Contradiction Subset): Improved from 34.1% to 89.4%.
  • This confirms the structural prior transfers to natural language inference, not just synthetic logic.

5. Significance and Implications

• Shift from Data-Centric to Structure-Centric: The paper challenges the assumption that scaling data alone yields reliable reasoning. It posits that structural verification mechanisms are necessary to enforce logical consistency.
• Process Over Prompting: Unlike prompt-only methods, Fusion-Conflict enforces verification as a learned structural constraint through SFT and DPO, making the verification step intrinsic to the model's generation process.
• Safety and Reliability: The framework provides a blueprint for "doubt-aware" AI systems capable of recognizing when premises are invalid. This is crucial for high-stakes domains like legal analysis and scientific discovery where "confident but wrong" answers are unacceptable.
• The "Circuit Breaker" Mechanism: The "Step 1: Verify" preamble acts as a functional circuit breaker, preventing the model's intuitive "System 1" from overriding factual reality, effectively bridging the gap between semantic-form invariance and logical-content reliability.

In conclusion, the paper demonstrates that by explicitly separating premise verification from deduction and reinforcing this separation via preference optimization, LLMs can overcome Logic Inertia and achieve verifiable, robust reasoning.