Spatial Probabilistic Temporal Databases
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Research in spatio-temporal probabilistic reasoning examines algorithms for handling data such as cell phone triangulation, GPS systems, movement prediction software, and other inexact but useful data sources. In this thesis I describe a probabilistic model theory for such data. The Spatial PrObabilistic Temporal database framework (or SPOT database framework) provides methods for interpreting, checking consistency, automatically revising, and querying such databases. This thesis examines two different semantics within the SPOT framework and presents polynomial-time consistency checking algorithms for both. It introduces several revision techniques for repairing inconsistent databases and compares them to the AGM Axioms for belief state revision; finding an algorithm that, by only changing the probability bounds in the SPOT atoms, can repair a SPOT database in polynomial time while still satisfying the AGM axioms. Also included is an investigation into optimistic and cautious versions of a selection query that returns all objects in a given region with at least (or at most) a certain probability. For these queries, I introduce an indexing structure akin to the R-tree called a SPOT tree, and show experiments where indexing speeds up selection with both artificial and real-world data. I also introduce query preprocessing techniques that bound the sets of solutions with both circumscribing and inscribing regions, and discover these to also provide query time improvements in practice. By covering semantics, consistency checking, database revision, indexing, and query preprocessing techniques for SPOT database, this thesis provides a significant step towards a SPOT database framework that may be applied to the sorts of real-world problems in the impressive amount of semi-accurate spatio-temporal data available today.