Conndence Relations and Ordinal Information 1

We deene conndence relations on Boolean lattices, which can be interpreted as ordinal representations of uncertainty or information. The set of the conndence relations on a given Boolean lattice can be ordered by set inclusion and thus is shown to form a complete meet-semilattice. We investigate and identify the maximal elements of this structure. Moreover, we prove that it is in particular an algebraic semilattice (or domain), and that its nite elements are precisely the nitely generated conndence relations. We also investigate the relationship with information systems. We deene duality and self-duality for conndence relations and show that similar conclusions can be reached if we restrict ourselves to conndence relations which are in particular self-dual. Finally, we discuss the possible incompleteness of conndence relations, and the relation between the abstract mathematical structures studied here, and other existing uncertainty models.