Affiliations: School of Applied Mathematics and Information Science, Higher School of Economics, Moscow, Russia, [email protected] | School of Applied Mathematics and Information Science, Higher School of Economics, Moscow, Russia, [email protected]
Note: [] We thank Florent Domenach for his careful reading, useful comments and suggestions. We thank Daniel Borchmann for providing us with a useful FCA library in Clojure dialect of LISP and for useful suggestions. We thank Fuad Aleskerov, Bernhard Ganter and Gleb Koshevoy for helpful discussions. We also thank the anonymous reviewers for very helpful remarks. This work was partially supported by the Russian Foundation for Basic Research, project no. 08-07-92497-NTsNIL_a. Address for correspondence: School of Applied Mathematics and Information Science, Higher School of Economics, Pokrovskii bd., 109028 Moscow, Russia
Note: [] We thank Florent Domenach for his careful reading, useful comments and suggestions. We thank Daniel Borchmann for providing us with a useful FCA library in Clojure dialect of LISP and for useful suggestions. We thank Fuad Aleskerov, Bernhard Ganter and Gleb Koshevoy for helpful discussions. We also thank the anonymous reviewers for very helpful remarks. This work was partially supported by the Russian Foundation for Basic Research, project no. 08-07-92497-NTsNIL_a.
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.
Keywords: Properties of Functions, Attribute Exploration, Implication Basis
