Probabilistic Belief Contraction

Authors:
Raghav Ramachandran;Arthur Ramer;Abhaya C. Nayak
Affiliations:
Department of Computing, Macquarie University, Sydney, Australia 2109;School of Computer Science and Engineering, University of New South Wales, Sydney, Australia 2052;Department of Computing, Macquarie University, Sydney, Australia 2109
Venue:
Minds and Machines
Year:
2012

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Abstract

Probabilistic belief contraction has been a much neglected topic in the field of probabilistic reasoning. This is due to the difficulty in establishing a reasonable reversal of the effect of Bayesian conditionalization on a probabilistic distribution. We show that indifferent contraction, a solution proposed by Ramer to this problem through a judicious use of the principle of maximum entropy, is a probabilistic version of a full meet contraction. We then propose variations of indifferent contraction, using both the Shannon entropy measure as well as the Hartley entropy measure, with an aim to avoid excessive loss of beliefs that full meet contraction entails.