By Bernhard Ganter, Sergei Obiedkov

This is the 1st textbook on characteristic exploration, its idea, its algorithms forapplications, and a few of its many attainable generalizations. characteristic explorationis priceless for buying based wisdom via an interactive approach, 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 relies on Formal suggestion research, a mathematical idea ofconcepts and thought hierarchies, and makes use of its expressive diagrams. The presentationis self-contained. It presents an advent to Formal thought Analysiswith emphasis on its skill to derive algebraic constructions from qualitative data,which will be represented in significant and specific graphics.

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Label the diagram. 23. 4 Consider the following diagram describing properties of natural numbers: prime square even odd cubic Label the diagram with as few numbers as possible to obtain a valid concept lattice diagram (consistent with the properties of numbers). Show the corresponding formal context. Is there any natural number that does not fit the diagram? 5 Give an example of a lattice with both top and bottom elements that is not complete. Hint: such a lattice must consist of an infinite number of elements.

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). 2 An example We illustrate the method by means of an example from elementary geometry. The objects of our example are seven triangles. 14. 4. 14: A formal context of triangles and their attributes. The pictures of the triangles have different scales 24 Chapter 1. Concept lattices 1. Write the attribute extents to a list.

We say that A is lectically smaller than B if the smallest element in which A and B differ belongs to B. Formally, A

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