By Bernhard Ganter, Sergei Obiedkov
This is the 1st textbook on characteristic exploration, its thought, its algorithms forapplications, and a few of its many attainable generalizations. characteristic explorationis precious for buying established wisdom via an interactive procedure, byasking queries to knowledgeable. Generalizations that deal with incomplete, defective, orimprecise information are mentioned, however the concentration lies on wisdom extraction from areliable info source.The approach relies on Formal idea research, a mathematical idea ofconcepts and notion hierarchies, and makes use of its expressive diagrams. The presentationis self-contained. It presents an advent to Formal notion Analysiswith emphasis on its skill to derive algebraic buildings from qualitative data,which should be represented in significant and unique graphics.
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Extra resources for Conceptual Exploration
Thus we can perfectly reconstruct the formal context from the diagram (“the original data”). Moreover, for each formal concept we can easily determine its extent and intent from the diagram. So in a certain sense, concept lattice diagrams are perfect. But there are, of course, limitations. 11. Is it correct? Is it complete? The answer is that, since a concept lattice faithfully unfolds the formal context, the information displayed in the lattice diagram can be only as correct and complete as the formal context is.
Again, the definition is inspired by the way humans usually order concepts in a subconcept– superconcept hierarchy: “pig” is a subconcept of “mammal”, because every pig is a mammal. 3. The algebra of concepts Definition 3 Let (A1 , B1 ) and (A2 , B2 ) be formal concepts of (G, M, I). We say that (A1 , B1 ) is a subconcept of (A2 , B2 ) and, equivalently, that (A2 , B2 ) is a superconcept of (A1 , B1 ) iff A1 ⊆ A2 . We use the ≤-sign to express this relation and thus have (A1 , B1 ) ≤ (A2 , B2 ) : ⇐⇒ A1 ⊆ A2 .
2. If A