 A major source of independent, game-theoretic perspectives on logic is the game semantics of computational logics (Abramsky 1997). In this setting, the status of logic games may change. Rather than being a mere pedagogical or exploratory device, to some, these games are considered the true meaning of logical constants. In this setting, infinite games are often the paradigm, standing for ongoing processes, rather than finite terminating games. This shows in the importance of infinite parity games for the modal μ-calculus, Venema (2008), as well as in the earlier-mentioned co-algebraic perspective on games. Baltag, van Benthem &amp; Westerståhl (forthcoming) discuss the outside-in perspective of co-algebraic game semantics as a viable general paradigm for linguistic meaning representing a significant shift in standard discussions of compositionality.