Probabilistic logics for objects located in space and time

Spatiotemporal databases can be used to efficiently store and retrieve information about objects moving in space and time. Probabilities are added to model the case where the locations are not known with certainty. A few years ago a new formalism was introduced to represent such information in the form of atomic formulas, each of which represents the probability (in the form of an interval because even the probabilities are not known precisely) that a particular object is in a particular location at a particular time. We extend this formalism to obtain several different probabilistic logics by adding logical operators. Furthermore, we axiomatize these logics, provide corresponding semantics, prove that the axiomatizations are sound and complete, and discuss decidability issues. While we relate these logics to previous axiomatizations of probabilistic logics, this article is self-contained: no prior knowledge of probabilistic logics is assumed.