Model-checking games for fixpoint logics with partial order models

We introduce model-checking games that allow local second-order power on sets of independent transitions in the underlying partial order models where the games are played. Since the one-step interleaving semantics of such models is not considered, some problems that may arise when using interleaving semantics are avoided and new decidability results for partial orders are achieved. The games are shown to be sound and complete, and therefore determined. While in the interleaving case they coincide with the local model-checking games for the μ-calculus (Lμ), in a noninterleaving setting they verify properties of Separation Fixpoint Logic (SFL), a logic that can specify in partial orders properties not expressible with Lμ. The games underpin a novel decision procedure for model-checking all temporal properties of a class of infinite and regular event structures, thus improving previous results in the literature