04762nam a22005895i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001500172050001300187072001600200072001600216072002300232072001500255072001500270100008600285245011600371250001800487264006900505300003400574336002600608337002600634338003600660347002400696505051300720520211301233650004703346650003103393650005403424650003303478650001903511650004203530650002603572650005103598650004603649650003003695650005803725650004603783700008303829710003403912773002603946776003603972776003604008776003604044856004604080912001404126912001504140999001704155978-3-031-63422-2DE-He21320251030112701.0cr nn 008mamaa240731s2024    sz |    s    |||| 0|eng d  a97830316342229978-3-031-63422-27 a10.1007/978-3-031-63422-22doi 4aQA76.9.D35 4aQ350-390 7aUMB2bicssc 7aGPF2bicssc 7aCOM0210002bisacsh 7aUMB2thema 7aGPF2thema1 aGanter, Bernhard.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98162010aFormal Concept Analysish[electronic resource] :bMathematical Foundations /cby Bernhard Ganter, Rudolf Wille.  a2nd ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXII, 370 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aPreface 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.  aFormal 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. . 0aData structures (Computer science).966708 0aInformation theory.957783 0aInformation storage and retrieval systems.965568 0aInformation modeling.981621 0aAlgebra.91501 0aComputer sciencexMathematics.964041 0aDiscrete mathematics.14aData Structures and Information Theory.96670924aInformation Storage and Retrieval.96557024aInformation Model.98162224aOrder, Lattices, Ordered Algebraic Structures.96950024aDiscrete Mathematics in Computer Science.1 aWille, Rudolf.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9816232 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303163421508iPrinted edition:z978303163423908iPrinted edition:z978303163424640uhttps://doi.org/10.1007/978-3-031-63422-2  aZDB-2-SCS  aZDB-2-SXCS  c62085d62085