Attribute Exploration of Properties of Functions on Sets

Authors:
Artem Revenko;Sergei O. Kuznetsov
Affiliations:
(Thanks to: Florent Domenach, Daniel Borchmann, Fuad Aleskerov, Bernhard Ganter, Gleb Koshevoy and the anonymous reviewers for very helpful remarks. This work was partially supported by the Russia ...;(Thanks to: Florent Domenach, Daniel Borchmann, Fuad Aleskerov, Bernhard Ganter, Gleb Koshevoy and the anonymous reviewers for very helpful remarks. This work was partially supported by the Russia ...
Venue:
Fundamenta Informaticae - Concept Lattices and Their Applications
Year:
2012

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Abstract

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. Example 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.