A metric conceptual space algebra

  • Authors:

  • Benjamin Adams;Martin Raubal

  • Affiliations:

  • Departments of Computer Science and Geography, University of California, Santa Barbara;Departments of Computer Science and Geography, University of California, Santa Barbara

  • Venue:
  • COSIT'09 Proceedings of the 9th international conference on Spatial information theory
  • Year:
  • 2009

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Abstract

The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.