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A framework for analyzing systems that contain contradictions without collapsing into triviality—that is, without allowing every statement to become provable. Inspired by paraconsistent logic, it studies how real‑world systems (legal codes, databases, belief networks, social systems) often harbor inconsistent information yet continue to function. The theory develops methods for reasoning productively with contradictions: separating them into manageable parts, tracking their sources, and preventing explosion (the principle that contradiction implies everything). It is used in AI, knowledge representation, regulatory analysis, and conflict resolution.
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