Extending Ladkin's algebra on non-convex intervals towards an algebra on union-of regions

Abstract

This paper proposes an extension of Ladkin's algebra on non-convex intervals towards the spatial dimension. Based on the concepts of adverbs, we introduce an algebra that qualifies topological relationships between regions composed of simple regions. These adverbs are flexible enough to apply on composite regions with an indefinite number of simple regions. A set of mutually exclusive and complete quantitative and temporal adverbs is also introduced for evolving composite regions. Since adverbs are widely used and understood by common sense reasoning, such an extended algebra provides a flexible method to analyse large spatial configurations.