Reasoning about Qualitative Spatial Relationships

In this paper, we consider various spatial relationships that are of general interest in pictorial database systems and other applications. We present a set of rules that allow us to deduce new relationships from a given set of relationships. A deductive mechanism using these rules can be used in query-processing systems that retrieve pictures by content. The given set of rules is shown to be sound; that is, the deductions are logically correct. The rules are also shown to be complete for three-dimensional systems; that is, every relationship that is implied by a given consistent set of relationships F is deducible from F using the given rules. In addition, we show that the given set of rules is incomplete for two-dimensional systems. We also present efficient algorithms for the deduction and reduction problems. The deduction problem consists of computing all the relationships deducible from a given set, while the reduction problem consists of computing a minimal subset of a given set of relationships that implies all the relationships in the given set.

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