A Theory of Granular Partitions

In M. Duckham, M. F. Goodchild & M. F. Worboys (eds.), Foundations of Geographic Information Science. London: Taylor & Francis. pp. 117-151 (2003)
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Abstract
We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it provides an account of how cells and subcells relate to objects in reality. We define a notion of well-formedness for partitions, and we give an account of what it means for a partition to project onto objects in reality. We continue by classifying partitions along three axes: (a) in terms of the degree of correspondence between partition cells and objects in reality; (b) in terms of the degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) in terms of the degree of completeness with which a partition represents this domain.
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References found in this work BETA
Parts of Classes.Lewis, David K.
Intentionality.Searle, J. R.
Parts of Classes.Potter, Michael
Holes and Other Superficialities.Casati, Roberto & Varzi, Achille C.

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