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Informational independence: Models and normal forms
Author(s) -
van der Gaag L. C.,
Meyer J.J. Ch.
Publication year - 1998
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/(sici)1098-111x(199801)13:1<83::aid-int7>3.0.co;2-t
Subject(s) - independence (probability theory) , computer science , artificial intelligence , mathematical economics , mathematics , statistics
The concept of informational independence plays a key role in most knowledge‐based systems. J. Pearl and his co‐researchers analysed the basic properties of the concept and formulated an axiomatic system for informational independence. This axiomatic system focuses on independences among mutually disjoint sets of variables. We show that in the context of probabilistic independence a focus on disjoint sets of variables can hide various interesting properties. To capture these properties, we enhance Pearl's axiomatic system with two additional axioms. We investigate the set of models of the thus enhanced system and show that it provides a better characterization of the concept of probabilistic independence than Pearl's system does. In addition, we observe that both Pearl's axiomatic system and our enhanced system offer inference rules for deriving new independences from an initial set of independence statements and as such allow for a normal form for representing independence. We address the normal forms ensuing from the two axiomatic systems for informational independence. © 1998 John Wiley & Sons, Inc.13: 83–109, 1998