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Abstract:
In this paper I define four sets of binary topological relations between one dimensional regions in a one-dimensional space: (1) boundary insensitive relations in a non-directed space, (2) boundary insensitive relations in a directed space, (3) boundary sensitive relations in a non-directed space, and (4) boundary sensitive relations in a directed space. For each of these sets of relations between exact regions I de- fine a corresponding set of relations between approximations of regions with respect to an underlying regional partition. I discuss syntactic and semantic generalizations of relations between exact regions to corresponding relations between approximations and show the equivalence of syntactic and semantic generalization.