A cartesian closed category of approximable concept structures

TitleA cartesian closed category of approximable concept structures
Publication TypeConference Paper
Year of Publication2004
AuthorsGuo-Qiang Zhang, Pascal Hitzler
Conference NameA cartesian closed category of approximable concept structures
Abstract

Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the two areas as outlined in [25]. Building on a new notion of approximable concept introduced by Zhang and Shen [26], this paper provides an appropriate notion of morphisms on formal contexts and shows that the resulting category is equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. Since the latter categories are cartesian closed, we obtain a cartesian closed category of formal contexts that respects both the context structures as well as the intrinsic notion of approximable concepts at the same time.

Full Text

Guo-Qiang Zhang and Pascal Hitzler, 'A cartesian closed category of approximable concept structures,' 12th International Conference on Conceptual Structures, ICCS 2004, pp.170-185.
pages: 170-185
year: 2004
venue name: 12th International Conference on Conceptual Structures, ICCS
hasURL: http://www.springerlink.com/content/67c0cm6aulnnmfmh/fulltext.pdf