Abstract
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.
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References
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Lawvere, F.W., Rosebrugh, R.: Sets for mathematics. Cambridge University Press, Cambridge (2003)
Goguen, J., Burstall, R.: Institutions: abstract model theory for specification and programming. Journal of the ACM 39 (1992)
Barwise, J., Seligman, J.: Information flow: the logic of distributed systems. Cambridge tracts in theoretical computer science, vol. 44. Cambridge University Press, Cambridge (1997)
Kent, R.E.: The information flow foundation for conceptual knowledge organization. In: Proc. of the 6th Int. Conf. of the International Society for Knowledge Organization (2000)
Kent, R.E.: Semantic integration in the Information Flow Framework. In: Kalfoglou, Y., et al. (eds.) Semantic Interoperability and Integration. Dagstuhl Seminar Proceedings 04391 (2005)
Pratt, V.: Chu spaces as a semantic bridge between linear logic and mathematics. Theoretical Computer Science 294, 439–471 (2003)
Krötzsch, M., Hitzler, P., Zhang, G.Q.: Morphisms in context. Technical report, AIFB, Universität Karlsruhe (2005), www.aifb.uni-karlsruhe.de/WBS/phi/pub/KHZ05tr.pdf
Erné, M.: Categories of contexts. Unpublished (2005); Rewritten version
Xia, W.: Morphismen als formale Begriffe, Darstellung und Erzeugung. PhD thesis, TH Darmstadt (1993)
Ganter, B.: Relational Galois connections. Unpublished manuscript (2004)
Kent, R.E.: Distributed conceptual structures. In: de Swart, H. (ed.) RelMiCS 2001. LNCS, vol. 2561, pp. 104–123. Springer, Heidelberg (2002)
Hitzler, P., Krötzsch, M., Zhang, G.Q.: A categorical view on algebraic lattices in formal concept analysis. Technical report, AIFB, Universität Karlsruhe (2004)
Krötzsch, M.: Morphisms in logic, topology, and formal concept analysis. Master’s thesis, Dresden University of Technology (2005)
Goguen, J.: Three perspectives on information integration. In: Kalfoglou, Y., et al. (eds.) Semantic Interoperability and Integration. Dagstuhl Seminar Proceedings 04391 (2005)
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Krötzsch, M., Hitzler, P., Zhang, GQ. (2005). Morphisms in Context. In: Dau, F., Mugnier, ML., Stumme, G. (eds) Conceptual Structures: Common Semantics for Sharing Knowledge. ICCS 2005. Lecture Notes in Computer Science(), vol 3596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11524564_15
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DOI: https://doi.org/10.1007/11524564_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27783-5
Online ISBN: 978-3-540-31885-9
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