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## GanterWille99

1. Bernhard Ganter & Rudolf Wille R
2. Formal concept analysis: Mathematical foundations
3. Springer 1999 QA171.5 G3513 1999
4. =THEORY MATHEMATICAL FORMAL LOGIC LATTICE CONCEPT
5. Given a set of objects X, a set of attributes Y, and a relation R:@(X><Y), then (X,Y,R) is called a formal context. If A is a subset of X then define A'={y:Y. for all x:A(x R y)}. Similarly B'={x:X.for all y:B( x R y)}. A formal concept is a pair (A, B) where A'=B and B'=A, and A is the extent and B the intent of concept (A,B). The subconcept_superconcept relation:(A1,B1) <= (A2,B2) iff A1 is a subset of A2. This defines a lattice of formal concepts.
6. Leads to a diagram showing the underlying structure of the relation R.
7. Given a table X><Y<>-> Z and by defining a scaling Z into (true, false) then a context can be defined.
8. See [ logic_42_Properties_of_Relation.html ] for some rough notes on Concept analysis.
9. Note. Theory has been used to aid the maintenance of software:

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