Distance Constraint Arrays: A Model for Reasoning on Intervals with Qualitative and Quantitative Distances

We outline a model of one-dimensional reasoning on interval relations with quantitative and qualitative distances. At the core of this model lie constraints on interval boundaries, partial ordering and subsumption relations on interval relations and interval boundary constraints, and the transformation of interval relations to interval boundary constraints and vice versa. By way of subsumption and approximation criteria on distance constraint arrays, a significant level of conceptual abstraction from the underlying interval boundary constraints is realized when new relations are inferred.

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