Conditionalization for Interval Probabilities

Conditionalization, i.e., computation of a conditional probability distribution given a joint probability distribution of two or more random variables is an important operation in some probabilistic database models. While the computation of the conditional probability distribution is straightforward when the exact point probabilities are involved, it is often the case that such exact point probability distributions of random variables are not known, but are known to lie in a particular interval. This paper investigates the conditionalization operation for interval probability distribution functions under a possible world semantics. In particular, given a joint probability distribution of two or more random variables, where the probability of each outcome is represented as an interval, we (i) provide formal model-theoretic semantics; (ii) define the operation of conditionalization and (iii) provide a closed form solution/efficient algorithm to compute the conditional probability distribution.