A Multi-Stage Rule-Chaining Framework for Compositional and Interpretable Cognitive Reasoning

Overview

The Abstraction and Reasoning Corpus (ARC) benchmarks cognitive generalization—the ability to infer and apply abstract rules from limited examples. In 2026, as ARC-AGI-2 has become a central yardstick for measuring machine intelligence beyond memorization, interpretable and compositional reasoning methods are increasingly in demand.

This paper presents a multi-stage rule-chaining framework that performs compositional reasoning across symbolic, structural, and conceptual levels. The architecture bridges symbolic reasoning and pattern synthesis, offering interpretable insight into how machines generalize cognitively.

Framework Architecture

The framework integrates three complementary solvers operating sequentially within a progressive fallback hierarchy, where each stage reuses prior reasoning traces to enhance interpretability and generalization:

1. Deterministic Rule Discovery Module — Induces atomic transformations through geometric, color, and object-based analysis.
2. Pattern-Composition Engine — Reconstructs outputs via block merging, repetition, and spatial heuristics.
3. Structural Abstraction Layer — Infers hierarchical and nested relationships across grids.



Results



• Training: Passed 995 out of 1000 tasks
• Intermediate Evaluation: 105 out of 120 tasks
• ARC-AGI-2 Test Set: Solved 230 out of 240 tasks
• Overall Accuracy: Exceeding 95%



The system achieved strong coverage across deterministic, compositional, and abstract categories.




Significance




These results suggest that rule chaining and hierarchical composition can advance machine reasoning toward transparent, human-aligned abstraction—without relying on task-specific tuning. As of 2026, this positions the approach as a notable contribution to the growing body of neuro-symbolic methods aimed at interpretable general intelligence.




Resources



• Code: Kaggle Notebook – 995 Tasks Solutions
• Dataset: ARC Prize 2025 – Kaggle Competition Data



Metadata



• Author: Deblina Kar
• Submitted: 9 September 2026
• Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
• Cite as: arXiv:2609.10654 [cs.AI]
• DOI: https://doi.org/10.48550/arXiv.2609.10654

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