Extending the relational model with uncertainty and ignorance

It has been widely recognized that in many real-life database applications there is growing demand to model uncertainty and ignorance. However the relational model does not provide this possibility. Through the years a number of efforts has been devoted to the capture of uncertainty and ignorance in databases. Most of these efforts attempted to capture uncertainty using the classic probability theory. As a consequence, the limitations of probability theory are inherited by these approaches, such as the problem of information loss. In this paper, we extend the relational model with uncertainty and ignorance without these limitations posed by the other approaches. Our approach is based on the so-called theory of belief functions, which may be considered as a generalization of probability theory. Belief functions have an attractive mathematical\ud underpinning and many intuitively appealing properties

Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the underlying representation of uncertainty. We give sound and complete axiomatizations for the logic in the case that the underlying representation is (a) probability, (b) sets of probability measures, (c) belief functions, and (d) possibility measures. We show that this logic is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures, but equi-expressive in the case of probability, belief, and possibility. Finally, we show that satisfiability for these logics is NP-complete, no harder than satisfiability for propositional logic.Comment: To appear in Journal of the AC