Modal Logics for Nominal Transition Systems

We formalize a uniform semantic substrate for a wide variety of process calculi where states and action labels can be from arbitrary nominal sets. A Hennessy-Milner logic for these systems is defined, and proved adequate for bisimulation equivalence. A main novelty is the construction of an infinitary nominal data type to model formulas with (finitely supported) infinite conjunctions and actions that may contain binding names. The logic is generalized to treat different bisimulation variants such as early, late and open in a systematic way.