Diagrammatic Transformation Processes on Two-dimensional Relational Maps

Abstract

Research on qualitative spatial reasoning has produced an impressive number of systems of relations for representing topological, ordinal and metrical information. In comparison, the number of reasoning procedures that has been proposed is rather limited. Most approaches simply rely on standard constraint propagation techniques such as the path consistency algorithm. Evidence from cognitive science indicates that human reasoners solve spatial relational inferences not by constraint satisfaction methods but by constructing and inspecting mental models in visuo-spatial working memory. From a computational point of view, this strategy combines the relational representations used in qualitative spatial reasoning with the local spatial transformations studied in diagrammatic reasoning. However, applying local transformations to arbitrary relational representations involves solving the intractable subgraph isomorphism problem. The paper describes a class of representations, relational maps, for which the problem becomes tractable and for which, as a consequence, diagrammatic inference is implementable by efficient local transformations.