Topological structures as a tool for formal modelling of rough sets

Abstract

Abstract-In the paper, we present the topological counterpart supporting rich formal apparatus describing properties of rough sets within one of the largest repositories of computerized mathematical knowledge, the Mizar Mathematical Library. The paper develops third and final (after lattice theory and the theory of general binary relations) planned path designed to be linked (via mechanisms of theory merging) with the theory of structures described by Pawlak in the early seventies of the previous century. We propose the revision of the existing topological apparatus offered by Mizar, and give the outline of the formalization of uniform spaces, important objects allowing for further representation of approximation spaces.

Developing Field Theory in Mizar

“…Mizar is the name for both the proof checker and the formal language in which definitions and proofs are written. Mizar has often been described in the literature, for example in [19], [13], [10], [12] and [3]. We therefore here give only a very rough description of Mizar.…”