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Automated Comparative Study of Some Generalized Rough Approximations

Grabowski Adam

Fundamenta Informaticae

2021

Vol. 179, nr 2

165--182

The paper contains some remarks on building automated counterpart of a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to arbitrary binary relation. Our focus was on translating rationality postulates for such operators by means of the Mizar system – the software and the database which allows for expressing and checking mathematical knowledge for the logical correctness. The main objective was the formal (and machine-checked) proof of Theorem 4.1 from A. Gomolińska’s paper “A Comparative Study of Some Generalized Rough Approximations ”, hence the present title. We provide also the discussion on how to make the presentation more efficient to reuse the reasoning techniques of the Mizar verifier.

Automated Discovery of Properties of Rough Sets

Grabowski A.

Fundamenta Informaticae

2013

Vol. 128, nr 1-2

66--79

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.