HENKIN QUANTIFIERS: LOGIC, GAMES, AND COMPUTATION

In this paper, we study the game-theoretic and computational repercussions of Henkin's partially ordered quantifiers [19]. After defining a game-theoretic semantics for these objects, we observe that tuning the parameter of absentmindedness gives rise to quantifier prefixes studied in [28]. In the interest of computation, we characterize the complexity class P-parallel to(NP) in terms of partially ordered quantifiers, by means of a proof different from Gottlob's [17]. We conclude with some research questions at the interface of logic, game theory, and complexity theory.