Relating Information and Proof

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.