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Modal operators on bounded residuated l-monoids
by
Dana Šalounová
Technical University Ostrava, Czech Republic
Bounded residuated lattice ordered monoids (Rl-monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo MV-algebras (or, equivalently, GMV-algebras) and pseudo BL-algebras (and so, particularly, MV-algebras and BL-algebras). Modal operators on Heyting algebras were studied by D. C. Macnab. Analogously, modal operators on MV-algebras and on bounded commutative Rl-monoids were considered recently. We generalize modal operators to bounded Rl- monoids which need not be commutative and investigate their properties also for further derived algebras.
Date received: April 27, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caug-15.