Measuring questions: relevance and its relation to entropy

Details Measuring questions: relevance and its relation to entropy Measuring questions: relevance and its relation to entropy

2004-09-17

arxiv.org/abs/physics/0409084v1

Physics

Data Analysis, Statistics and Probability

8 pages, 1 figure. Presented to the MaxEnt 2004 meeting in Garching Germany. To be published in: R. Fischer, V. Dose (eds.), B

Scientific paper

10.1063/1.1835251

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a valuation called relevance or bearing, which is a measure of the degree to which one question answers another. Richard Cox conjectured that this degree can be expressed as a generalized entropy. With the assistance of yet another important result from Janos Aczel, I show that this is indeed the case, and that the resulting inquiry calculus is a natural generalization of information theory. This approach provides a new perspective on the Principle of Maximum Entropy.

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