  The AGM postulates by Alchourr\'{o}n, G\"{a}rdenfors, and Makinson continue
to represent a cornerstone in research related to belief change. We generalize
the approach of Katsuno and Mendelzon (KM) for characterizing AGM base revision
from propositional logic to the setting of (multiple) base revision in
arbitrary monotonic logics. Our core result is a representation theorem using
the assignment of total - yet not transitive - "preference" relations to belief
bases. We also provide a characterization of all logics for which our result
can be strengthened to preorder assignments (as in KM's original work).
