Games in Philosophical Logic

Semantic games are an important evaluation method for a wide range of logical languages, and are frequently resorted to when traditional methods do not easily apply. A case in point is a family of independence-friendly (IF) logics, allowing regulation over information flow in formulas, amounting to the failure of perfect information in semantic games associated with IF formulas, and giving rise to informationally independent logical components. The mechanism of informational independence is studied in this paper. For example, we note that the imperfect information of players is often accompanied by the game-theoretic phenomenon of imperfect recall. We reply to a couple of misunderstandings that have occurred in the literature concerning the relation of IF first-order logic and game-theoretic semantics, intuitionism, constructivism, truth-definitions, negation, mathematical prose, and the status of set theory. By straightening out these misunderstandings, we also hope to show, at least partially, the importance semantic games and IF logics have in philosophical logic.