  We present a complete logic for reasoning with functional dependencies (FDs)
with semantics defined over classes of commutative integral partially ordered
monoids and complete residuated lattices. The dependencies allow us to express
stronger relationships between attribute values than the ordinary FDs. In our
setting, the dependencies not only express that certain values are determined
by others but also express that similar values of attributes imply similar
values of other attributes. We show complete axiomatization using a system of
Armstrong-like rules, comment on related computational issues, and the
relational vs. propositional semantics of the dependencies.
