Abstract 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 µcalculus, 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.