Studia Logica

, Volume 69, Issue 3, pp 381–409

A Necessary Relation Algebra for Mereotopology

Authors

  • Ivo DÜntsch
    • School of Information and Software EngineeringUniversity of Ulster
  • Gunther Schmidt
    • Department of Computer ScienceUniversity of the Federal Armed Forces Munich
  • Michael Winter
    • Department of Computer ScienceUniversity of the Federal Armed Forces Munich
Article

DOI: 10.1023/A:1013892110192

Cite this article as:
DÜntsch, I., Schmidt, G. & Winter, M. Studia Logica (2001) 69: 381. doi:10.1023/A:1013892110192

Abstract

The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T0 topological space with an additional "contact relation" C defined by xCy ⇔ x ∩ ≠ Ø

A (possibly) more general class of models is provided by the Region Connection Calculus (RCC) of Randell et al. We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the RCC, and hence, in any standard model of mereotopology. It follows that the expressiveness of the RCC in relational logic is much greater than the original 8 RCC base relations might suggest. We also interpret these 25 relations in the the standard model of the collection of regular open sets in the two-dimensional Euclidean plane.

mereologymereotopologyrelation algebraqualitative spatial reasoning
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Copyright information

© Kluwer Academic Publishers 2001