Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets
: J. Järvinen, S. Radeleczki
Publisher: Akademiai Kiado Rt.
: 2020
: Acta Mathematica Hungarica
: Acta Mathematica Hungarica
: 160
: 1
: 175
: 196
: 22
: 0236-5294
: 1588-2632
DOI: https://doi.org/10.1007/s10474-019-00985-8
: https://research.utu.fi/converis/portal/detail/Publication/43785240
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.
