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In the context of formal verification in general and model checking inparticular, parity games serve as a mighty vehicle: many problems are encodedas parity games, which are then solved by the seminal algorithm by Jurdzinski.In this paper we identify the essence of this workflow to be the notion ofprogress measure, and formalize it in general, possibly infinitary,lattice-theoretic terms. Our view on progress measures is that they are tonested/alternating fixed points what invariants are to safety/greatest fixedpoints, and what ranking functions are to liveness/least fixed points. That is,progress measures are combination of the latter two notions (invariant andranking function) that have been extensively studied in the context of(program) verification.  We then apply our theory of progress measures to a general model-checkingframework, where systems are categorically presented as coalgebras. Theframework's theoretical robustness is witnessed by a smooth transfer from thebranching-time setting to the linear-time one. Although the framework can beused to derive some decision procedures for finite settings, we also expect theproposed framework to form a basis for sound proof methods for someundecidable/infinitary problems.

Lattice-Theoretic Progress Measures and Coalgebraic Model Checking (with Appendices)