Formal Concept Analysis : Mathematical Foundations / by Bernhard Ganter, Rudolf Wille.

Format:

Book

Author/Creator:

Ganter, Bernhard, author.

Wille, Rudolf, author.

Language:

English

Subjects (All):

Data structures (Computer science).

Information theory.

Information storage and retrieval systems.

Information modeling.

Algebra.

Computer science--Mathematics.

Computer science.

Discrete mathematics.

Data Structures and Information Theory.

Information Storage and Retrieval.

Information Model.

Order, Lattices, Ordered Algebraic Structures.

Discrete Mathematics in Computer Science.

Local Subjects:

Data Structures and Information Theory.

Information Storage and Retrieval.

Information Model.

Order, Lattices, Ordered Algebraic Structures.

Discrete Mathematics in Computer Science.

Physical Description:

1 online resource (375 pages)

Edition:

2nd ed. 2024.

Place of Publication:

Springer Nature 2024

Summary:

Formal Concept Analysis is a field of applied mathematics based on the math­ematization of concept and conceptual hierarchy. It thereby activates math­ematical 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. 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, Formal Concept Analysis has fully emerged, sparking a multitude of publications for which the first edition of this textbook established itself as the standard reference in the literature, with a total of 10000+ citations. This is the second edition, revised and extended, of the textbook published originally in German (1996) and translated into English (1999), giving a systematic presentation of the mathematical foundations while also focusing on their possible applications for data analysis and knowledge processing. In times of digital knowledge processing, formal methods of conceptual analysis are gaining in importance. The book makes the basic theory for such methods accessible in a compact form, and presents graphical methods for representing concept systems that have proved themselves essential in communicating knowledge. The textbook complements each chapter with further notes, references and trends, putting the work in modern context and highlighting potential directions for further research. Additionally, the book contains an entirely new chapter on contextual concept logic, including a section on description logics and relational concept analysis. As such, it should be a valuable resource for students, instructors and researchers at the crossroads of subject areas like Applied and Discrete Mathematics, Logics, Theoretical Computer Science, Knowledge Processing, Data Science, and is meant to be used both for research and in class, as a teaching resource. .

Contents:

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.

Notes:

Includes bibliographical references and index.

ISBN:

9783031634222

3031634225