A Mathematical Theory of Pragmatic Information

תקציר מקורי באנגליתarXiv:2609.10986v4 Announce Type: replace-cross Abstract: 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 lossless source coding, channel coding, and rate-distortion theorems that extend Shannon's results. These measures quantify decision uncertai