NDLI: Heyting Mereology as a Framework for Spatial Reasoning

Content Provider	Springer Nature Link
Author	Mormann, Thomas
Copyright Year	2012
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.
Starting Page	137
Ending Page	164
Page Count	28
File Format	PDF
ISSN	11221151
Journal	Axiomathes
Volume Number	23
Issue Number	1
e-ISSN	15728390
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-01-26
Publisher Place	Dordrecht
Access Restriction	Subscribed
Subject Keyword	Mereology Heyting algebras Co-Heyting algebras Topology Boundary Interior parts Contact relation Representations Philosophy Ontology Linguistics (general) Cognitive Psychology Logic
Content Type	Text
Resource Type	Article
Subject	Philosophy Mathematics

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