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Morphisms in Context

Markus KrötzschPascal Hitzler, Guo-Qiang Zhang

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
Ausgabe: 3596
Reihe: Lecture Notes in Computer Science
Seiten: 223-237
Verlag: Springer, Berlin
Referierte Veröffentlichung

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.

Download: Media:2005_902_Krötzsch_Morphisms_in_Co_1.pdf





Semantic Web, Domaintheorie, Formale Begriffsanalyse, Wissensrepräsentationssprachen, Logik