  We introduce negation under the stable model semantics in DatalogMTL - a
temporal extension of Datalog with metric temporal operators. As a result, we
obtain a rule language which combines the power of answer set programming with
the temporal dimension provided by metric operators. We show that, in this
setting, reasoning becomes undecidable over the rational timeline, and
decidable in EXPSPACE in data complexity over the integer timeline. We also
show that, if we restrict our attention to forward-propagating programs,
reasoning over the integer timeline becomes PSPACE-complete in data complexity,
and hence, no harder than over positive programs; however, reasoning over the
rational timeline in this fragment remains undecidable. Under consideration in
Theory and Practice of Logic Programming (TPLP).
