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Attribute Exploration of Properties of Functions on Sets

Revenko A., Kuznetsov S. O.

Fundamenta Informaticae

2012

Vol. 115, nr 4

377-394

An approach for studying relations between properties of functions on sets is proposed. The approach is based on Attribute Exploration. 16 properties of functions are considered, among them monotonicity, idempotency, path independence, exchange properties, convexity, etc. Exam- ple functions are partially computer generated on the powersets of sets with 2, 3 and 4 elements. Attribute Exploration is run on contexts where objects are functions and attributes are 16 function properties. Minimal implication bases are presented. The list of proved implications is presented and discussed.

Knowledge Acquisition under Incomplete Knowledge using Methods from Formal Concept Analysis: Part I

Holzer M.

Fundamenta Informaticae

2004

Vol. 63, nr 1

1--39

Formal contexts with unknown entries can be represented by three-valued contexts K = (G,M, {x,o,?},I), where a question mark indicates that it is not known whether the object g ∈G has the attribute m ∈M. To describe logical formulas between columns of such incomplete contexts the Kripke-semantics are used for propositional formulas over the set M of attributes. Attribute implications are considered as special propositional formulas. If a context is too large to be fully represented, an interactive computer algorithm may help the user to get maximal information (with respect to his knowledge) about the valid attribute implications of the unknown context. This computer algorithm is called "attribute exploration''.

Knowledge Acquisition under Incomplete Knowledge using Methods from Formal Concept Analysis: Part II

Holzer M.

Fundamenta Informaticae

2004

Vol. 63, nr 1

41--63

Attribute exploration is an interactive computer algorithm which helps the expert to get informations about the attribute implications of a formal context. In the part I of this paper (see [H04]) an algorithm for attribute exploration with incomplete knowledge was presented. In this part we prove the main results of the algorithm: At the end of the attribute exploration the expert gets maximal information with respect to his knowledge about the unknown universe: He gets a list of implications which are certainly valid, a list of implications which are possibly valid, a list of counterexamples against the implications which are certainly not valid and a list of fictitious counterexamples against the implications which he answered by `"unknown''. He only has to check the implications which he answered by `"unknown'' and if he can decide for each of these implications whether it is valid or not, he gets complete knowledge about the implications of the context.