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Weighted labelled transition systems (WLTSs) are an established meta-modelaiming to provide general results and tools for a wide range of systems such asnon-deterministic, stochastic, and probabilistic systems. In order to encompassprocesses combining several quantitative aspects, extensions of the WLTSframework have been further proposed, state-to-function transition systems(FuTSs) and uniform labelled transition systems (ULTraSs) being two prominentexamples. In this paper we show that this hierarchy of meta-models collapseswhen studied under the lens of bisimulation-coherent encodings. Takingadvantage of these reductions, we derive a fully abstract Hennessy-Milner-stylelogic for FuTSs, i.e., which characterizes quantitative bisimilarity, from afully-abstract logic for WLTSs.

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