dorsal/arxiv
View SchemaMeasuring questions: relevance and its relation to entropy
| Authors | Kevin H. Knuth |
|---|---|
| Categories | |
| ArXiv ID | physics/0409084 |
| URL | https://arxiv.org/abs/physics/0409084 |
| DOI | 10.1063/1.1835251 |
Abstract
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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"abstract": "The Boolean lattice of logical statements induces the free distributive\nlattice of questions. Inclusion on this lattice is based on whether one\nquestion answers another. Generalizing the zeta function of the question\nlattice leads to a valuation called relevance or bearing, which is a measure of\nthe degree to which one question answers another. Richard Cox conjectured that\nthis degree can be expressed as a generalized entropy. With the assistance of\nyet another important result from Janos Aczel, I show that this is indeed the\ncase, and that the resulting inquiry calculus is a natural generalization of\ninformation theory. This approach provides a new perspective on the Principle\nof Maximum Entropy.",
"arxiv_id": "physics/0409084",
"authors": [
"Kevin H. Knuth"
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"doi": "10.1063/1.1835251",
"title": "Measuring questions: relevance and its relation to entropy",
"url": "https://arxiv.org/abs/physics/0409084"
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