Automated Discovery of Properties of Rough Sets

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.

[1]  Jouni Järvinen,et al.  Lattice Theory for Rough Sets , 2007, Trans. Rough Sets.

[2]  Laurent Vigneron Automated Deduction Techniques for Studying Rough Algebras , 1998, Fundam. Informaticae.

[3]  William Zhu,et al.  Relationship between generalized rough sets based on binary relation and covering , 2009, Inf. Sci..

[4]  Adam Naumowicz,et al.  Mizar in a Nutshell , 2010, J. Formaliz. Reason..

[5]  Adam Grabowski,et al.  On the Lattice of Intervals and Rough Sets , 2009, Formaliz. Math..

[6]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

[7]  Adam Grabowski,et al.  Rough Concept Analysis - Theory Development in the Mizar System , 2004, MKM.

[8]  William Zhu,et al.  Generalized rough sets based on relations , 2007, Inf. Sci..

[9]  Zdzisław Pawlak Automatyczne dowodzenie twierdzeń , 1965 .

[10]  Anna Gomolinska,et al.  On Certain Rough Inclusion Functions , 2008, Trans. Rough Sets.

[11]  Z. Pawlak Rough Sets: Theoretical Aspects of Reasoning about Data , 1991 .

[12]  Freek Wiedijk,et al.  Formal proof -- getting started , 2008 .

[13]  Andrzej Skowron,et al.  Tolerance Approximation Spaces , 1996, Fundam. Informaticae.

[14]  Adam Grabowski,et al.  Translating Mathematical Vernacular into Knowledge Repositories , 2005, MKM.

[15]  Yiyu Yao,et al.  Comparison of Rough-Set and Interval-Set Models for Uncertain Reasoning , 1996, Fundam. Informaticae.

[16]  Josef Urban,et al.  Automated reasoning and presentation support for formalizing mathematics in Mizar , 2010, AISC'10/MKM'10/Calculemus'10.