M. Dube and M. Egenhofer, An Ordering of Convex Topological Relations, in: N.Xioa, M.P. Kwan, M. Goodchild, and S. Shekhar (eds.), Geographic Information Science — Seventh International Conference, GIScience 2012, Columbus, OH, Lecture Notes in Computer Science, Vol. 7478, Springer, pp. 72-86, September 2012.
Topological relativity is a concept of interest in geographic information theory. One way of assessing the importance of topology in spatial reasoning is to analyze commonplace terms from natural language relative to conceptual neighborhood graphs, the alignment structures of choice for topological relations. Sixteen English-language spatial prepositions for regionregion relations were analyzed for their corresponding topological relations, each of which was found to represent a convex subset within the conceptual neighborhood graph of the region-region relations, giving rise to the construction of the convex ordering of region-region relations. The resulting lattice of the convex subgraphs enables an algorithmic approach to explaining unknown prepositions.