Reductions for Transition Systems at Work: Deriving a Logical Characterization of Quantitative Bisimulation

Weighted labelled transition systems (WLTSs) are an established (meta-)model aiming to provide general results and tools for a wide range of systems such as non-deterministic, stochastic, and probabilistic systems. In order to encompass processes combining several quantitative aspects, extensions of the WLTS framework have been further proposed, state-to-function transition systems (FuTSs) and uniform labelled transition systems (ULTraSs) being two prominent examples. In this paper we show that this hierarchy of meta-models collapses when studied under the lens of bisimulation-coherent encodings. Taking advantage of these reductions, we derive a fully abstract Hennessy-Milner-style logic for FuTSs, i.e., which characterizes quantitative bisimilarity, from a fully-abstract logic for WLTSs.