Qualitative Spatial Logics for Buffered Geometries

Abstract

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 σ ∈ 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 briefl y 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.