On the connection between many-valued contexts and general geometric structures

Authors:
Tim B. Kaiser
Affiliations:
Institut für Algebra, Technische Universität Dresden, Dresden, Germany 01062
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2010

Citing 3
Cited 0

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CLA'06 Proceedings of the 4th international conference on Concept lattices and their applications
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ICCS'05 Proceedings of the 13th international conference on Conceptual Structures: common Semantics for Sharing Knowledge

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Abstract

We study the connection between certain many-valued contexts and general geometric structures. The known one-to-one correspondence between attribute-complete many-valued contexts and complete affine ordered sets is used to extend the investigation to 驴-lattices, class geometries, and lattices with classification systems. 驴-lattices are identified as a subclass of complete affine ordered sets, which exhibit an intimate relation to concept lattices closely tied to the corresponding context. Class geometries can be related to complete affine ordered sets using residuated mappings and the notion of a weak parallelism. Lattices with specific sets of classification systems allow for some sort of "reverse conceptual scaling".