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Lower and upper concept lattices. (English) Zbl 1349.06011

Summary: Formal Concept Analysis is a mathematical theory of data analysis using formal contexts and concept lattices. In this paper, two new types of concept lattices are introduced by using notions from domain theory (in particular, Hoare and Smyth powerdomains). Based on a Galois connection, we prove the fundamental theorem of the Formal Concept Analysis, as well as other properties of “lower” and “upper” formal concepts. In this way, we provide new models to represent and retrieve the information in data and knowledge systems.

MSC:

06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68T30 Knowledge representation
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