Graded Modalities and Resource Bisimulation

The logical characterization of the strong and the weak (ignoring silent actions) versions of resource bisimulation are studied. The temporal logics we introduce are variants of Hennessy-Milner Logics that use graded modalities instead of the classical box and diamond operators. The considered strong bisimulation induces an equivalence that, when applied to labelled transition systems, permits identifying all and only those systems that give rise to isomorphic unfoldings. Strong resource bisimulation has been used to provide nondeterministic interpretation of finite regular expressions and new axiomatizations for them. Here we generalize this result to its weak variant.