FILTERS AND DEDUCTIVE SYSTEMS ON RESIDUATED MULTILATTICES

We continue the study of the residuated operations in the framework of hyperstructures. We focus on the case of a multilattice as underlying algebraic structure and introduce the notions of filter and deductive system. They differ from the analogous concepts in a pocrim due to the connection to congruence relations. Finally, we prove that the set of filters of a residuated multilattice is a complete lattice.