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Logic of linear constraints for spatial propagation

Geographic information often involves constraints on spatial and/or temporal information, which can be represented in terms of real-valued variables. In many problems these constraints are linear, and there is a developing literature on reasoning with linear constraints in GIS.

One of the main advantages of expressing reasoning with linear constraints as a logic is that it makes it relatively easy to generalise many uncertainty formalisms, both numerical and logical, for reasoning with uncertain linear constraints; this work has numerous potential applications in GIS.

Even if constraints are not linear, they may sometimes be approximated by linear constraints, e.g., using polygons to approximately represent the boundaries of spatial objects. The main contributions of this work have been the expression of reasoning with linear inequality constraints as logic, with a very simple proof theory, which is sound and complete for finite sets of constraints.

Reported by

Keele University
Department of Computer Science
United Kingdom
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