In this paper, we study the method of closure games, a game-theoretic valuation method for languages of self-referential truth developed by the author. We prove two theorems which jointly establish that the method of closure games characterizes all 3- and 4-valued strong Kleene fixed points in a novel, informative manner. Among others, we also present closure games which induce the minimal and maximal intrinsic fixed point of the strong Kleene schema.

Game-theoretic semantics, Kripke's theory of truth, Self-referential truth,
Notre Dame Journal of Formal Logic
Erasmus School of Philosophy

Wintein, S. (2016). From closure games to strong Kleene truth. Notre Dame Journal of Formal Logic, 57(2), 153–179. doi:10.1215/00294527-3346590