Temporal Probabilistic Object Bases

There are numerous applications where we have to deal with temporal uncertainty associated with objects. For example, financial prediction programs often use complex object models and are parameterized by time and uncertainty (e.g., when will a given loan default?). Likewise, in transportation logistics, object models are used to describe objects involved in the transportation process (e.g., vehicles and shipments), and detailed probability distributions exist on shipping and delay times. Thus, in such applications, the ability to automatically store and manipulate time, probabilities, and objects is important. In this paper, we propose a data model and algebra for temporal probabilistic object bases. The data model allows us to associate with each event e set of possible time points T, and with each time point t \in T , an interval for the probability that e occurred at t. We distinguish between explicit object base instances, where the sets of time points along with their probability intervals are simply enumerated, and implicit ones, where the sets of time points are expressed by constraints and their probability intervals by probability distribution functions. Thus, implicit object base instances are succinct representations of explicit ones; they allow for an efficient implementation of algebraic operations, while their explicit counterparts make defining algebraic operations easy. We define the algebraic operations of selection, restricted selection, renaming, projection, extraction, natural join, Cartesian product, conditional join, and the set operations of intersection, union, and difference on both explicit and implicit object base instances. We show that each operation on implicit object base instances correctly implements its counterpart on explicit object base instances.