Download e-book for kindle: Conceptual Exploration by Bernhard Ganter, Sergei Obiedkov

By Bernhard Ganter, Sergei Obiedkov

This is the 1st textbook on characteristic exploration, its concept, its algorithms forapplications, and a few of its many attainable generalizations. characteristic explorationis invaluable for buying based wisdom via an interactive method, byasking queries to knowledgeable. Generalizations that deal with incomplete, defective, orimprecise information are mentioned, however the concentration lies on wisdom extraction from areliable details source.The strategy is predicated on Formal suggestion research, a mathematical thought ofconcepts and notion hierarchies, and makes use of its expressive diagrams. The presentationis self-contained. It offers an advent to Formal notion Analysiswith emphasis on its skill to derive algebraic buildings from qualitative data,which may be represented in significant and targeted graphics.

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Download PDF by Bernhard Ganter, Sergei Obiedkov: Conceptual Exploration

This can be the 1st textbook on characteristic exploration, its conception, its algorithms forapplications, and a few of its many attainable generalizations. characteristic explorationis priceless for buying dependent wisdom via an interactive method, byasking queries to knowledgeable. Generalizations that deal with incomplete, defective, orimprecise info are mentioned, however the concentration lies on wisdom extraction from areliable details resource.

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If the result is a set that is not yet in the list, then extend the list by this set. With the extended list, continue to build all pairwise intersections. 3. If for any two sets of the list their intersection is also in the list, then extend the list by the set G (provided it is not yet contained in the list). The list now contains all concept extents (and nothing else). 4. For every concept extent A in the list compute the corresponding intent A to obtain a list of all formal concepts (A, A ) of (G, M, I).

Similarly, (A1 , B1 )∨(A2 , B2 ) is a superconcept of (A1 , B1 ) and of (A2 , B2 ) and is a subconcept of any common superconcept of these two formal concepts. Instead of “least common superconcept” we usually say supremum, and instead of “greatest common subconcept” we use the word infimum. With some practice, one can read off the infimum and supremum from the lattice diagram. 11 and follow the descending paths from the corresponding nodes in the diagram. There is always a unique highest point where these paths meet, that is, the highest concept that is below both, namely, the infimum.

12. Apart from the top element, 1, and the bottom element, 0, it contains seven elements: a, b, c, d, e, f, and g. All but c and f are supremum-irreducible; thus, the set G = {a, b, d, e, g} is supremum-dense in L. The set M = {a, e, f, g} is infimum-dense. The Basic Theorem tells us that the concept lattice of the context (G, M, I), where g I m whenever g ≤ m in L, is isomorphic to L. 12. We leave it as an easy exercise to check that its concept lattice is indeed isomorphic to L. We conclude with a simple observation that often helps finding errors in concept lattice diagrams.

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