Relating Information and Knowledge
摘要
The basic notion of information in mathematics is the entropy of a random variable, and the value of entropy is a number. Individual pieces of information are not analyzed explicitly, and the theory works well as it is. In colloquial speech “information” is usually a statement, a piece of information. Such a statement, that is mathematically a logical formula, should be justified by a proof, that constitutes the knowledge we refer to. The formula with the proof represents, in a way, the information received. How to measure its quantity? The paper discusses this question for a simple model of such knowledge. The approach uses an entropy-like function called entropic weight. Entropic weight, contrary to the classical entropy, is monotone and corresponds to our intuition in the context under treatment. The paper is mainly a conceptual discussion.