Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets
arXiv:1806.09203 · doi:10.1007/s10474-019-00985-8
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.
arXiv commentThe title of the work has changed from the first version. Section 5 is largely rewritten. New references are also added
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