Raghav Ramachandran

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.

In this paper we investigate three approaches to iterated contraction, namely: the Moderate (or Priority) contraction, the Natural (or Conservative) contraction, and the Lexicographic contraction. We characterise these three contraction functions using certain, arguably plausible, properties of an iterated contraction function. While we provide the characterisation of the first two contraction operations using rationality postulates of the standard variety for iterated contraction, we found doing the same for the Lexicographic contraction more challenging. We provide its characterisation using a variation of Epistemic ranking function instead.