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REPRESENTING REGULAR PSEUDOCOMPLEMENTED KLEENE ALGEBRAS BY TOLERANCE-BASED ROUGH SETS

Part of: Boolean algebras (Boolean rings) Distributive lattices Artificial intelligence (68Txx) Lattices

Published online by Cambridge University Press:  04 December 2017

JOUNI JÄRVINEN Open the ORCID record for JOUNI JÄRVINEN [Opens in a new window]  and
SÁNDOR RADELECZKI
JOUNI JÄRVINEN*
Affiliation:
Sirkankuja 1, 20810 Turku, Finland email [email protected]
SÁNDOR RADELECZKI*
Affiliation:
Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary email [email protected]
*
✉[email protected]
✉[email protected]
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Abstract

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We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.

Keywords

Kleene algebraalgebraic latticepseudocomplemented latticeregular double p-algebrarough settolerance relationirredundant covering

MSC classification

Primary: 06B15: Representation theory
Secondary: 06D15: Pseudocomplemented lattices 06D30: De Morgan algebras, L ukasiewicz algebras 68T37: Reasoning under uncertainty 06D20: Heyting algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 105 , Issue 1 , August 2018 , pp. 57 - 78
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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