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
dx.doi.org/10.1215/00294527-3346590, hdl.handle.net/1765/84546
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