Description Logic Knowledge and Action Bases (KABs) have been recently
introduced as a mechanism that provides a semantically rich representation of
the information on the domain of interest in terms of a DL KB and a set of
actions to change such information over time, possibly introducing new objects.
In this setting, decidability of verification of sophisticated temporal
properties over KABs, expressed in a variant of first-order mu-calculus, has
been shown. However, the established framework treats inconsistency in a
simplistic way, by rejecting inconsistent states produced through action
execution. We address this problem by showing how inconsistency handling based
on the notion of repairs can be integrated into KABs, resorting to
inconsistency-tolerant semantics. In this setting, we establish decidability
and complexity of verification.