A note on proximity spaces and connection based mereology

  • Authors:

  • Dimiter Vakarelov;Ivo Düntsch;Brandon Bennett

  • Affiliations:

  • Sofia University, Sofia, Bulgaria;University of Ulster, Newtownabbey, BT, N. Ireland;University of Leeds, Leeds, England

  • Venue:
  • Proceedings of the international conference on Formal Ontology in Information Systems - Volume 2001
  • Year:
  • 2001

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Abstract

Representation theorems for systems of regions have been ofinterest for some time, and various contexts have been used forthis purpose: Mormann [17] has demonstrated the fruitfulness of themethods of continuous lattices to obtain a topologicalrepresentation theorem for his formalisation of Whiteheadianontological theory of space; similar results have been obtained byRoeper [20]. In this note, we prove a topological representationtheorem for a connection based class of systems, using methods andtools from the theory of proximity spaces. The key novelty is a newproximity semantics for connection relations.