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 granular 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 histories.
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Smith, B., Brogaard, B. Quantum Mereotopology. Annals of Mathematics and Artificial Intelligence 36, 153–175 (2002). https://doi.org/10.1023/A:1015860121607
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DOI: https://doi.org/10.1023/A:1015860121607