Bernhard Ganter, Rudolf Wille

Formal Concept Analysis (eBook, PDF)

Mathematical Foundations
Übersetzer: Franzke, C.

• Format: PDF

Produktbeschreibung

Formal Concept AllalY.5is is a field of applied mathematics based on the math ematization of concept and conceptual hierarchy. It thereby activates math ematical thinking for conceptual data analysis and knowledge processing. The underlying notion of "concept" evolved early in the philosophical theory of concepts and still has effects today. For example, it has left its mark in the German standards DIN 2:)30 and DIN 2;3:)1. In mathematics it played a special role during the emergence of mathematical logic in the 19th century. Subsequently, however, it had virtually no impact on mathematical thinking. It was not until 1979 that the topic was revisited and treated more thoroughly. Since then, through a large number of contributions, Formal Concept Analysis has obtained such breadth that a systematic presentation is urgently needed, but can no longer be realized in one volume. Therefore, the present book foruse:':! on the mathematical foundations of Formal Concept Analysis, which ran be regarded chiefly as a branch of ap plied lattice theory. A series of examples serves to demonstrate the utility of the lnathematical definitions and results; in particular, to show how Formal Concept Analysis can be used for the conceptual unfolding of data contexts. These examples do not play the role of case studies in data analysis. A is intended for a comprehensive treatment of methods of separate volume conceptual data and knowledge processing. The general foundations of For mal Concept Analysis will also be treated separately.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 284
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642598302
• Artikelnr.: 53171958

Autorenporträt

Bernhard Ganter is Emeritus Professor of Mathematics at Technische Universität Dresden, Germany. His main research field is Formal Concept Analysis. Before being appointed to Dresden in 1993, he was a member of R. Wille's working group and contributed to the development of Formal Concept Analysis. He is co-founder of the "Mathematics Adventure Land" exhibition in Dresden, which has been a success since 2008.   Rudolf Wille (2 November 1937 - 22 January 2017) was professor of Mathematics (General Algebra) from 1970 to 2003 at Technische Universität Darmstadt, Germany. He is cofounder of the celebrated theory of Formal Concept Analysis, a field of mathematics that applies mathematical lattice theory to organize data based on objects and their shared attributes. An accomplished musician, he also made contributions to Mathematics in Music, Mathematical Pedagogy and the Philosophy of Science, and was a leading scholar in the concept lattice research community.  

Inhaltsangabe

Preface to the first edition.- Preface to the second edition.- Acknowledgements.- 0. Order-theoretic foundations.- 1. Concept lattices of formal contexts.- 2. Determination and representation.- 3. Parts, factors, and bonds.- 4. Decompositions of concept lattices.- 5. Constructions of concept lattices.- 6. Properties of concept lattices.- 7. Context comparison and conceptual measurability.- 8. Contextual concept logic.- References.- Formal contexts and concept lattices in this book.- Index.