Qualitative Spatial Logics for Buffered Geometries

This paper describes a series of new qualitative spatial logics for checking consistency of sameAs and partOf matches between spatial objects from different geospatial datasets, especially from crowd-sourced datasets. Since geometries in crowd-sourced data are usually not very accurate or precise, we buffer geometries by a margin of error or a level of tolerance a E R≥0, and define spatial relations for buffered geometries. The spatial logics formalize the notions of 'buffered equal' (intuitively corresponding to `possibly sameAs'), 'buffered part of' ('possibly partOf'), 'near' (`possibly connected') and 'far' ('definitely disconnected'). A sound and complete axiomatisation of each logic is provided with respect to models based on metric spaces. For each of the logics, the satisfiability problem is shown to be NP-complete. Finally, we briefly describe how the logics are used in a system for generating and debugging matches between spatial objects, and report positive experimental evaluation results for the system