Quantum Mereotopology

  • Authors:
  • Barry Smith;Berit Brogaard

  • Affiliations:
  • Department of Philosophy, Center for Cognitive Science and NCGIA, University at Buffalo, NY 14260, USA E-mail: phismith@buffalo.edu;Department of Philosophy, Southern Illinois University at Edwardsville, IL 62026, USA E-mail: brogaar@attglobal.net

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 2002

Quantified Score

Hi-index 0.00

Visualization

Abstract

While mereotopology – the theory of boundaries, contact and separation built up on a mereological foundation – has found fruitful applications in the realm of qualitative spatial reasoning, it faces problems when its methods are extended to deal with those varieties of spatial and non-spatial reasoning which involve a factor of granularity. This is because granularity cannot easily be represented within a mereology-based framework. We sketch how this problem can be solved by means of a theory of igranular partitions, a theory general enough to comprehend not only the familiar sorts of spatial partitions but also a range of coarse-grained partitions of other, non-spatial sorts. We then show how these same methods can be extended to apply to finite sequences of granular partitions evolving over time, or to what we shall call coarse- and fine-grained ihistories.