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Lattice duality: The origin of probability and entropy
 In press: Neurocomputing
, 2005
"... Bayesian probability theory is an inference calculus, which originates from a generalization of inclusion on the Boolean lattice of logical assertions to a degree of inclusion represented by a real number. Dual to this lattice is the distributive lattice of questions constructed from the ordered set ..."
Abstract

Cited by 19 (6 self)
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Bayesian probability theory is an inference calculus, which originates from a generalization of inclusion on the Boolean lattice of logical assertions to a degree of inclusion represented by a real number. Dual to this lattice is the distributive lattice of questions constructed from the ordered set of downsets of assertions, which forms the foundation of the calculus of inquiryâ€”a generalization of information theory. In this paper we introduce this novel perspective on these spaces in which machine learning is performed and discuss the relationship between these results and several proposed generalizations of information theory in the literature.
Toward QuestionAsking Machines: The Logic of Questions and the Inquiry Calculus
"... For over a century, the study of logic has focused on the algebra of logical statements. This work, first performed by George Boole... ..."
Abstract
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For over a century, the study of logic has focused on the algebra of logical statements. This work, first performed by George Boole...