The Abstraction and Reasoning Corpus (ARC) measures cognitive generalization—the ability to infer and apply abstract rules from few examples. This paper introduces a multi‑stage rule‑chaining framework that performs compositional reasoning across symbolic, structural, and conceptual levels. The architecture integrates three complementary solvers: a deterministic rule discovery module that induces atomic transformations via geometric, color, and object analysis; a pattern‑composition engine that rebuilds outputs through block merging, repetition, and spatial heuristics; and a structural abstraction layer that infers hierarchical and nested relationships across grids. The solvers run sequentially within a progressive fallback hierarchy, each stage reusing the reasoning trace of the previous one to enhance interpretability and generalization. Experiments trained successfully on 995 of 1000 tasks, evaluated 105 of 120 tasks, and solved 230 of 240 ARC‑AGI‑2 test tasks, achieving an overall accuracy above 95%. The design bridges symbolic reasoning with pattern synthesis, offering interpretable insight into cognitive generalization and showing that rule chaining and hierarchical composition can advance machine reasoning toward transparent, human‑aligned abstraction without task‑specific tuning.
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