Morphisms in Context
Published: 2005 Juli
Herausgeber: Frithjof Dau, Marie-Laure Mugnier and Gerd Stumme
Buchtitel: Conceptual Structures: Common Semantics for Sharing Knowledge. Proceedings of the 13th International Conference on Conceptual Structures, ICCS '05, Kassel, Germany, July 2005
Reihe: Lecture Notes in Computer Science
Verlag: Springer, Berlin
Morphisms constitute a general tool for modelling complex
relationships between mathematical objects on a large scale. In Formal Concept Analysis (FCA), morphisms can therefore be used for the study of structural properties of the 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, which includes the study of dual bonds, scale measures, infomorphisms and their respective relations to Galois connections. We summarize our results in a concept lattice that displays all relationships between the considered morphisms. The purpose of this foundational work is to provide a basis for future applications of FCA in ontology research and similar areas, where morphisms provide a way to formalize the interplay between distributed knowledge bases.