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REPRESENTING REGULAR PSEUDOCOMPLEMENTED KLEENE ALGEBRAS BY TOLERANCE-BASED ROUGH SETS

Part of: Artificial intelligence (68Txx) Lattices Boolean algebras (Boolean rings) Distributive 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 jouni.kalervo.jarvinen@gmail.com
SÁNDOR RADELECZKI*
Affiliation:
Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary email matradi@uni-miskolc.hu
*
✉jouni.kalervo.jarvinen@gmail.com
✉matradi@uni-miskolc.hu
Rights & Permissions [Opens in a new window]

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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