Maintaining Spatial Relations in an Incremental Diagrammatic Reasoner

This paper describes an architecture for dynamically handling spatial relations in an incremental, nonmonotonic diagrammatic reasoning system. The architecture represents jointly exhaustive and pairwise disjoint (JEPD) spatial relation sets as nodes in a dependency network. These spatial relation sets include interval relations, relative orientation relations, and connectivity relations, but in theory could include any JEPD spatial relation sets. This network then caches dependencies between low-level spatial relations, allowing those relations to be easily assumed or retracted as visual elements are added or removed from a diagram. For example, in the architecture’s Undo mechanism, the dependency network can quickly reactivate cached spatial relations when a previously-deleted element is restored. As part of this work, we describe how the system supports higher-level reasoning, including support for creating default assumptions. We also describe how this system was integrated with an existing drawing program and discuss its possible use in diagrammatic and geographic reasoning.