Lattice Theory for Rough Sets - An Experiment in Mizar

Rough sets is a well-known approach to incomplete or imprecise data. In the paper we briefly report how this framework was successfully encoded with the help of one of the leading computer proof assistants in the world. Thanks to their abstract and flexible character based essentially on binary relations, lattices as a basic viewpoint appeared a very feasible one in the case of rough sets. We focus on lattice-theoretical aspects of rough sets to enable the application of external theorem provers like EQP or Prover9 as well as to translate them into TPTP format widely recognized in the world of automated proof search. We wanted to have a clearly written, possibly formal, although informal as a rule, paper authored by a specialist from the discipline another than lattice theory. It appeared that Lattice theory for rough sets by Jouni Järvinen [11] (LTRS) was quite a reasonable choice to be a testbed for the current formalization both of lattices and of rough sets in Mizar.