This paper deals with the notion of approximate probabilistic bisimulation (APB) relation for discrete-time labeled Markov Chains (LMC). In order to provide a quantified upper bound on a metric over probabilistic realizations for LMC, we exploit the structure and properties of the APB and leverage the mathematical framework of Markov set- Chains. Based on this bound, the article proves that the existence of an APB implies the preservation of robust PCTL formulae, which are formulae that allow being properly relaxed or strengthened, according to the underlying APB. This leads to a notion of robustness for probabilistic model checking. Copyright 2012 ACM.