A Logic of Part and Whole for Buffered Geometries

We propose a new qualitative spatial logic for reasoning about part-whole relations between geometries (sets of points) represented in different geospatial datasets, in particular crowd-sourced datasets. Since geometries in crowd-sourced data can be less inaccurate or precise, we buffer geometries by a margin of error or level of tolerance sigma, and define part-whole relation for buffered geometries. The relations between geometries considered in the logic are: buffered part of (BPT), Near and Far. We provide a sound and complete axiomatisation of the logic with respect to metric models and show that its satisfiability problem is NP-complete.