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

Conference: ICLR 2026 arXiv: 2512.06393 Code: https://github.com/14H034160212/lemo Area: LLM Reasoning Keywords: logic inertia, contradiction detection, dual-process reasoning, structural robustness, rule-based reasoning

TL;DR

This paper identifies the phenomenon of "logic inertia" in LLMs—whereby models continue along learned reasoning trajectories even when presented with contradictory premises, reducing accuracy to 0.0—and proposes the Conflict-Aware Fusion dual-process architecture, which enforces premise verification prior to reasoning execution, achieving 100% accuracy on contradiction detection.

Background & Motivation

Background: LLMs perform well on multi-step logical reasoning benchmarks (benchmark accuracy of 1.0), yet these benchmarks typically evaluate reasoning under normal conditions without examining robustness when the rule system is perturbed.

Limitations of Prior Work: Existing evaluations conflate language competence with logical robustness. There is also a lack of diagnostic frameworks capable of isolating the individual effects of missing rules, redundant rules, and contradictory premises within a unified setting.

Key Challenge: Whether LLMs perform genuine logical reasoning or merely simulate it via pattern matching. When the structural integrity of a rule system is compromised—particularly through contradiction injection—the answer is the latter: all tested models collapse to 0.0 accuracy under contradictory conditions.

Goal: (a) Establish a systematic structural robustness evaluation framework; (b) identify and formalize the phenomenon of "logic inertia"; (c) design a reasoning framework that eliminates logic inertia.

Key Insight: The Cognitive Structure Hypothesis—reliable multi-step reasoning requires an explicit structural separation between premise verification and deductive execution, an inductive bias entirely absent from current end-to-end training paradigms.

Core Idea: Enforce a "verify-before-reason" structural constraint during inference—first applying System 2 to detect contradictions, then System 1 to execute reasoning, with a halt triggered upon contradiction detection.

Method

Overall Architecture

Three components: (1) a structural robustness benchmark featuring four controlled perturbation stress tests; (2) a dual-process reasoning architecture enforcing verification-prior-to-reasoning Chain-of-Thought structure; and (3) a two-stage optimization pipeline comprising structured SFT followed by DPO alignment.

Key Designs

1. Structural Robustness Benchmark (4 Stress Tests):

   • Variant 1: Redundant rule removal — the conclusion remains unchanged; tests the model's tolerance for redundant information.
   • Variant 2: Critical rule removal — the reasoning chain is broken; tests the model's ability to detect insufficient evidence.
   • Variant 3: Contradiction injection — evidence contradicting existing facts is introduced; tests contradiction detection.
   • Variant 4: Multiple equivalence law stacking — rules are rewritten via logically equivalent transformations; tests invariance to surface-level form.
   • Design Motivation: Each variant controls a single structural property derived from the same standard rule system, ensuring that performance differences are attributable to reasoning robustness rather than domain shift.

2. Dual-Process Reasoning Architecture:

   • Function: Enforces a two-stage structure within the CoT generation pathway.
   • Step 1 (System 2): Premise verification — checks premise completeness and consistency, and detects contradictions.
   • Step 2 (System 1): Conditional execution — deductive reasoning is performed only if Step 1 passes; "Halt Reasoning" is triggered upon contradiction detection.
   • Design Motivation: Transforms verification from an optional behavior into a mandatory structural step, breaking the inertia of "reasoning over verification."

3. Two-Stage Optimization Pipeline:

   • Stage 1: Structured SFT — trains on 11,200 instances (comprising standard, perturbed, and contradictory variants), with all samples mandatorily prefixed with "Step 1: Verify Facts," making premise checking a default procedure.
   • Stage 2: DPO Logic Alignment — constructs preference pairs: correct halting at contradictions ≻ continuing unsupported reasoning. This directly penalizes "hallucination shortcuts" and reinforces disciplined termination behavior.
   • Design Motivation: SFT establishes the verification structure; DPO reinforces contradiction detection behavior.

Loss & Training

• SFT: Standard autoregressive loss + LoRA (r=8, α=16), lr=2e-5, 3 epochs.
• DPO: Preference pairs (verify + halt vs. continue reasoning), directly optimizing policy-preference alignment.
• Models: BERT-base, Qwen2-1.5B, TinyLlama-1.1B, all fine-tuned with LoRA.

Key Experimental Results

Main Results

Method	Base Acc	Var 2 (Rule Removal)	Var 3 (Contradiction)
Stage 1 (SFT Baseline)	0.512	0.250	0.210
DPO (Direct Alignment)	0.475	0.267	0.510
CoT (Standard)	0.500	0.390	0.865
Mixed-Aug (Data Augmentation)	0.525	0.405	0.972
Fusion-LRA (Conflict-Aware SFT)	0.988	0.753	0.705
Fusion-Conflict (Full)	1.000	0.735	1.000

Ablation Study

Configuration	Base	Var 3 (Contradiction)	Note
All baselines (no Fusion)	1.000	0.000	Logic inertia: complete collapse under contradiction
+ SFT pre-training	~0.53	0.000	SFT alone cannot resolve contradictions
+ CoT	0.500	0.865	CoT helps but is insufficient
+ Fusion-LRA (SFT only)	0.988	0.705	Verification structure yields significant improvement
+ Fusion-Conflict (SFT+DPO)	1.000	1.000	Logic inertia fully eliminated

Key Findings

• Universality of logic inertia: BERT, Qwen2, and TinyLlama all achieve 0.0 accuracy under contradictory conditions—this is not a model-specific failure but a structural deficiency of the current LLM training paradigm.
• Robustness asymmetry: Models are highly stable under semantics-preserving transformations (Variant 4) yet collapse entirely under contradictions, indicating that models can recognize logical equivalence but cannot detect logical contradiction.
• External validation via Human Last Exam: All top-tier models, including GPT-4-level systems, also fail on constructed contradictory cases, confirming this as a general problem.
• Synergistic effect of verification structure and DPO: Neither SFT alone (0.705) nor DPO alone (0.510) suffices for contradiction detection; only their combination achieves 1.000.

Highlights & Insights

• Formalization of logic inertia: This work is the first to name and formalize this failure mode—LLMs prioritize completing the reasoning chain over verifying reasoning premises. This insight has far-reaching implications for AI safety.
• Precision of the dual-process architecture: The design placing System 2 before System 1 maps directly onto dual-process theory from cognitive science, translating a psychological concept into an engineerable AI architecture.
• Verification as a structural constraint: Rather than training models to "learn to verify," the approach makes models "required to verify"—internalizing verification as a mandatory precondition for reasoning through prompt structure and DPO reinforcement.

Limitations & Future Work

• Evaluation is conducted solely on controlled rule systems of limited scale (100 base instances), without validation on large-scale natural language reasoning benchmarks.
• Model scale is small (largest: Qwen2-1.5B); whether logic inertia persists in larger models remains to be verified.
• The dual-process architecture relies on prompt structure design; generalization to diverse reasoning tasks (mathematics, code, etc.) is unclear.
• Accuracy on Variant 2 (critical rule removal) remains only 0.735, indicating that insufficient-evidence scenarios are not yet fully resolved.

Related Work & Insights

• vs. Standard CoT: CoT encourages models to "think more" but does not guarantee "verify before thinking"; it reaches only 0.865 under contradictory conditions.
• vs. ChatLogic (external symbolic engine): ChatLogic relies on an external Prolog engine for reasoning verification, whereas this work internalizes verification into the model's own reasoning process.
• vs. Reversal Curse research: The Reversal Curse reveals the absence of bidirectional reasoning; Logic Inertia reveals the absence of premise verification—both serve as evidence that LLMs do not perform genuine reasoning.

Rating

• Novelty: ⭐⭐⭐⭐ — The proposal and formalization of the "logic inertia" concept carries significant value.
• Experimental Thoroughness: ⭐⭐⭐ — The evaluation scale is limited (100 instances), model sizes are small, and large-scale validation is lacking.
• Writing Quality: ⭐⭐⭐⭐ — Problem definition is clear, and the motivation for the dual-process architecture is well-reasoned.
• Value: ⭐⭐⭐⭐ — Exposes a fundamental deficiency in LLM reasoning with important implications for AI safety and reliable inference.

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