A1 Refereed original research article in a scientific journal

Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets



Authors: J. Järvinen, S. Radeleczki

Publisher: Akademiai Kiado Rt.

Publication year: 2020

Journal: Acta Mathematica Hungarica

Journal name in source: Acta Mathematica Hungarica

Volume: 160

Issue: 1

First page : 175

Last page: 196

Number of pages: 22

ISSN: 0236-5294

eISSN: 1588-2632

DOI: https://doi.org/10.1007/s10474-019-00985-8

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/43785240


Abstract

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 phrasespseudocomplemented Kleene algebra regular double p-algebra Stone identity prime filter rough set tolerance induced by an irredundant covering


Keywords:
prime filter, pseudocomplemented Kleene algebra, regular double p-algebra, rough set, Stone identity, tolerance induced by an irredundant covering

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Last updated on 26/11/2024 06:24:22 PM