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Synergy as the failure of distributivity (2404.03455v3)
Published 4 Apr 2024 in cs.IT, math.IT, physics.bio-ph, and physics.data-an
Abstract: The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. It resolves the persistent self-contradiction of information decomposition theory and reinstates it as a primary route toward a rigorous definition of emergence. Our results suggest that non-distributive variants of set theory may be used to describe emergent physical systems.
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