From Closure Games to Strong Kleene Truth

Abstract

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.