04985nam a22006495i 4500 978-3-031-63422-2 DE-He213 20251030112701.0 cr nn 008mamaa 240731s2024 sz | s |||| 0|eng d 9783031634222 978-3-031-63422-2 10.1007/978-3-031-63422-2 doi QA76.9.D35 Q350-390 UMB bicssc GPF bicssc COM021000 bisacsh UMB thema GPF thema Ganter, Bernhard. author. aut http://id.loc.gov/vocabulary/relators/aut 81620 Formal Concept Analysis [electronic resource] : Mathematical Foundations / by Bernhard Ganter, Rudolf Wille. 2nd ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XII, 370 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. . Data structures (Computer science). 66708 Information theory. 57783 Information storage and retrieval systems. 65568 Information modeling. 81621 Algebra. 1501 Computer science Mathematics. 64041 Discrete mathematics. Data Structures and Information Theory. 66709 Information Storage and Retrieval. 65570 Information Model. 81622 Order, Lattices, Ordered Algebraic Structures. 69500 Discrete Mathematics in Computer Science. Wille, Rudolf. author. aut http://id.loc.gov/vocabulary/relators/aut 81623 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031634215 Printed edition: 9783031634239 Printed edition: 9783031634246 https://doi.org/10.1007/978-3-031-63422-2 ZDB-2-SCS ZDB-2-SXCS 62085 62085