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Abstract

This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thouroughly and illuminated by means of numerous examples. Since computers are being used ever more widely for knowledge processing, formal methods for conceptual analysis are gaining in importance. This book makes the basic theory for such methods accessible in a compact form

Content

Order theoretical foundations. - Concept lattices of contexts. - Determination and presentation. - Parts and factors. - Analysis, construction and properties of concept lattices. - Context comparison and conceptual measurability

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Abstract

We give an overview over the computational tools for conceptional structures that have emerged from the theory of Formal Concept Analysis, with emphasis on basic ideas rather than technical details. We describe what we mean by conceptual computations, and try to convince the reader that an elaborate formalization is a necessary precondition. Claiming that Formal Concept Analysis provides such a formal background, we present as examples two well known algorithms in very simple pseudo code. These earl be used for navigating in a lattice, thereby supporting some prototypical tasks of conceptual computation. We refer to some of the many more advanced methods, discuss how to compute with limited precision and explain why in the case of incomplete knowledge the conceptual approach is more efficient than a combinatorial one. Utilizing this efficiency requires skillful use of the formalism. We present two results that lead in this direction

Series

Lecture notes in computer science; vol.1867: Lecture notes on artificial intelligence

Source

Conceptual structures: logical, linguistic, and computational issues. 8th International Conference on Conceptual Structures, ICCS 2000, Darmstadt, Germany, August 14-18, 2000. Ed.: B. Ganter et al

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Abstract

This first textbook in the field of formal concept analysis provides a systematic presentation of the mathematical foundations and their relation to applications in informatics, especially data analysis and knowledge processing

Content

Order theoretical foundations. - Concept lattices of contexts. - Determination and presentation. - Parts and factors. - Analysis, construction and properties of concept lattices. - Context comparison and conceptual measurability

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Source

Classification as a tool of research. Ed.: W. Gaul u. M. Schader

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Source

Applications of combinatorics and graph theory to the biological and social sciences. Ed.: F. Roberts