Automated Discovery of Properties of Rough Sets

Abstract

The computer certification of rough sets (the translation in a way understandable by machines) seems to be far beyond the test phase. To assure the feasibility of the approach, we try to encode selected problems within rough set theory and as the testbed of already developed foundations -and in the same time as a payoff of the established framework -we shed some new light on the well-known question of generalization of rough sets and the axiomatization of approximation operators in terms of (various types of) binary relations. We show how much the human work can be enhanced with the use of automatic tools, without loosing too much time for the translation. Although the syntax is understandable by the computer, it offers relative flexibility and expressive power of the formal language. A. Grabowski / Automated Discovery of Properties of Rough Setsbe reduced to the first order logic, but the application of existing provers to the questions which arose in rough set theory is not that straightforward as one can expect to be.We deal with the Zhu's paper [16] on the axiomatization of various generalizations of rough sets with respect to ordinary binary relation properties. It was not surprising that the original Pawlak's approach [9] would soon be generalized, and so did Skowron and Stepaniuk [10], Yao [14], and Zhu [16], among others. But similar work, although precious and carefully driven by human hand, can be done by computers.Rough sets deliver important tools to discover knowledge from databases, it is now especially valuable taking into account the amount of stored information and the form of the records. Digitization of mathematical journals gets more and more popular, and it is often the case of:• new material, when papers can be published faster, so information exchange, and hence research is more efficient and accessible -here the well-known example could be Springer's Online First;

Enhancement of properties in Mizar

“…• collecting new knowledge realized by: (a) developing background knowledge to prepare a comprehensive database for practicing mathematicians and for educational purposes; (b) formalizing entire mathematical books (Gierz et al, 1980;Bancerek & Rudnicki, 2002); (c) formalizing well-known theorems (Abad & Abad, 1999); and (d) developing new theories (Grabowski, 2014;Grabowski, 2013;Grabowski & Jastrzebska, 2010).…”