%0 Conference Paper
%B 13th International Conference on Conceptual Structures, ICCS '05
%D 2005
%T Morphisms in Context
%A Markus Krotzsch
%A Guo-Qiang Zhang
%A Pascal Hitzler
%X Morphisms constitute a general tool for modelling complex relationships between mathematical objects in a disciplined fashion. In Formal Concept Analysis (FCA), morphisms can be used for the study of structural properties of knowledge represented in formal contexts, with applications to data transformation and merging. In this paper we present a comprehensive treatment of some of the most important morphisms in FCA and their relationships, including dual bonds, scale measures, infomorphisms, and their respective relations to Galois connections. We summarize our results in a concept lattice that cumulates the relationships among the considered morphisms. The purpose of this work is to lay a foundation for applications of FCA in ontology research and similar areas, where morphisms help formalize the interplay among distributed knowledge bases.
%B 13th International Conference on Conceptual Structures, ICCS '05
%C Kassel, Germany
%P 223-237
%G eng
%0 Conference Paper
%B A cartesian closed category of approximable concept structures
%D 2004
%T A cartesian closed category of approximable concept structures
%A Guo-Qiang Zhang
%A Pascal Hitzler
%X 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.
%B A cartesian closed category of approximable concept structures
%G eng