Relating Information and Proof

Anatol Slissenko

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arXiv · 2205.07635

Relating Information and Proof

Anatol Slissenko

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Abstract

In mathematics information is a number that measures uncertainty (entropy) based on a probabilistic distribution, often of an obscure origin. In real life language information is a datum, a statement, more precisely, a formula. But such a formula should be justified by a proof. I try to formalize this perception of information. The measure of informativeness of a proof is based on the set of proofs related to the formulas under consideration. This set of possible proofs (`a knowledge base') defines a probabilistic measure, and entropic weight is defined using this measure. The paper is mainly conceptual, it is not clear where and how this approach can be applied.

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Anatol Slissenko. 2022-05-12. Relating Information and Proof. https://arxiv.org/abs/2205.07635

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