Attribute Exploration of Properties of Functions on Ordered Sets

An approach for studying relations between properties of functions on ordered 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 automatically generated on the powersets of sets with 2, 3 and 4 elements. The protocol of Attribute Exploration, which is run on examples of functions as objects and 16 function properties as attributes, is considered. The current Duquenne-Guigues implication base is presented. The list of proved implications is presented and discussed.