Heyting Mereology as a Framework for Spatial Reasoning

Axiomathes 23 (1):137- 164 (2013)
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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.

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Thomas Mormann
Ludwig Maximilians Universität, München (PhD)

Citations of this work

Topological Models of Columnar Vagueness.Thomas Mormann - 2022 - Erkenntnis 87 (2):693 - 716.
Intuitionistic mereology.Paolo Maffezioli & Achille C. Varzi - 2021 - Synthese 198 (Suppl 18):4277-4302.

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References found in this work

What Is Classical Mereology?Paul Hovda - 2009 - Journal of Philosophical Logic 38 (1):55 - 82.
Fiat and Bona Fide Boundaries.Barry Smith & Achille C. Varzi - 2000 - Philosophy and Phenomenological Research 60 (2):401-420.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.

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