LEADER 04903nam 22007095 450 001 9910878044003321 005 20240731125721.0 010 $a3-031-63422-5 024 7 $a10.1007/978-3-031-63422-2 035 $a(MiAaPQ)EBC31574465 035 $a(Au-PeEL)EBL31574465 035 $a(CKB)33566231300041 035 $a(DE-He213)978-3-031-63422-2 035 $a(EXLCZ)9933566231300041 100 $a20240731d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFormal Concept Analysis $eMathematical Foundations /$fby Bernhard Ganter, Rudolf Wille 205 $a2nd ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (375 pages) 311 $a3-031-63421-7 327 $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. 330 $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. . 606 $aData structures (Computer science) 606 $aInformation theory 606 $aInformation storage and retrieval systems 606 $aInformation modeling 606 $aAlgebra 606 $aComputer science$xMathematics 606 $aDiscrete mathematics 606 $aData Structures and Information Theory 606 $aInformation Storage and Retrieval 606 $aInformation Model 606 $aOrder, Lattices, Ordered Algebraic Structures 606 $aDiscrete Mathematics in Computer Science 615 0$aData structures (Computer science). 615 0$aInformation theory. 615 0$aInformation storage and retrieval systems. 615 0$aInformation modeling. 615 0$aAlgebra. 615 0$aComputer science$xMathematics. 615 0$aDiscrete mathematics. 615 14$aData Structures and Information Theory. 615 24$aInformation Storage and Retrieval. 615 24$aInformation Model. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 615 24$aDiscrete Mathematics in Computer Science. 676 $a005.73 676 $a003.54 700 $aGanter$b Bernhard$0117759 701 $aWille$b Rudolf$055209 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910878044003321 996 $aFormal Concept Analysis$94189142 997 $aUNINA