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arXiv · 1806.09203

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

Jouni Järvinen·Sándor Radeleczki
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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.

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Jouni Järvinen, Sándor Radeleczki. 2019-05-12. Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets. https://doi.org/10.1007/s10474-019-00985-8

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