Heyting Mereology as a Framework for Spatial Reasoning

Axiomathes 23 (1):137- 164 (2013)
Authors
Thomas Mormann
University of the Basque Country
Abstract
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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DOI 10.1007/s10516-011-9180-x
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References found in this work BETA

What Is Classical Mereology?Paul Hovda - 2009 - Journal of Philosophical Logic 38 (1):55 - 82.
On the Calculus of Relations.Alfred Tarski - 1941 - Journal of Symbolic Logic 6 (3):73-89.
Mereotopology: A Theory of Parts and Boundaries.Barry Smith - 1996 - Data and Knowledge Engineering 20 (3):287–303.

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