Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets - J. Järvinen; S. Radeleczki (Akademiai Kiado Rt., 2022)
We introduce Kleene–Varlet spaces as partially ordered sets equipped with a polarity satisfying certain additional conditions. By applying Kleene–Varlet spaces, we prove that each regular pseudocomplemented Kleene algebra is isomorphic to a subalgebra of the rough set regular pseudocomplemented Kleene algebra defined by a tolerance induced by an irredundant covering. We also characterize the Kleene–Varlet spaces corresponding to the regular pseudocomplemented Kleene algebras satisfying the Stone identity.
Key words and phrases
pseudocomplemented Kleene algebra regular double p-algebra Stone identity prime filter rough set tolerance induced by an irredundant covering