Modal-Like Operators in Boolean Lattices, Galois Connections and Fixed Points

Authors:
Jouni Järvinen;Michiro Kondo;Jari Kortelainen
Affiliations:
Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland. E-mail: jouni.jarvinen@utu.fi;School of Information Environment, Tokyo Denki University, Inzai 270-1382, Japan;Laboratory of Applied Mathematics, Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland
Venue:
Fundamenta Informaticae
Year:
2007

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Abstract

In this work, four modal-like operators on Boolean lattices are introduced and their theory is presented from lattice-theoretical, topological and algebraic point of view. It is also shown how rough set approximation operators, modal operators in temporal logic, and linguistic modifiers determined by L-sets can be interpreted as modal-like operators.