MDM is generally considered in the context of
database systems, and intranets within enterprise networks, but
is certainly about managing models just as ontologies are. At
this level the differences are mostly about the differences
between database system technologies and semantic system
technologies. These differences are well known.
On another level ontologies, or should I say the greater
ontology community, focuses more on the scope of use. MDM
systems are still localized, and thus the models are still
vetted within the context of an enterprise and its use cases.
The focus/goals of the semantic community is to develop models
that will be vetted on the broadest scale possible, starting
perhaps in localized communities but branching outward when
and where possible. So the goals are similar, and the kinds of
people working the problems have a similar mindset and
approach, but the tools and languages are different, and the
focus (sometimes because of those tools and languages) is
different.
Logic is one way to build models but it is only one way
so I do not think that bringing it into the discussion is on
point.