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A Mathematical Theory of Pragmatic Information

arXiv · AI, language, vision and robotics · article · Sep 10, 2026 · UTC

We propose a mathematical theory of pragmatic information that connects communication, control, and decision-making. Its central notion is the isoteleia mapping, which formalizes equifinality: distinct semantic paths that lead to the same optimal action are treated as pragmatically equivalent. This mapping yields a three-tier hierarchy of syntactic, semantic, and pragmatic information, in which each successive abstraction removes distinctions that are irrelevant to the task. We then define pragmatic entropy, up/down pragmatic mutual information, channel capacity, and rate-distortion, and prove

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