Axiomathes 23 (1):137- 164 (2013)
In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator.
|Keywords||Mereology Heyting algebras Co-Heyting algebras Topology (Non-)Tangential Parts Contact Relation Boundary Representation|
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References found in this work BETA
Parts and Places. The Structures of Spatial Representation.Roberto Casati & Achille C. Varzi - 1999 - MIT Press.
Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology.Achille C. Varzi - 1996 - Data and Knowledge Engineering 20:259–286.
Mereotopology: A Theory of Parts and Boundaries.Barry Smith - 1996 - Data and Knowledge Engineering 20 (3):287–303.
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