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

Article type: Research Article

Authors: Järvinen, Jouni | Kondo, Michiro | Kortelainen, Jari

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

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.

Keywords: Galois connections, Closure operators, Fixed points, Boolean lattices with additional operators

Journal: Fundamenta Informaticae, vol. 76, no. 1-2, pp. 129-145, 2007