Notre Dame Journal of Formal Logic

From Closure Games to Strong Kleene Truth

Stefan Wintein

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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.

Article information

Notre Dame J. Formal Logic, Volume 57, Number 2 (2016), 153-179.

Received: 19 May 2011
Accepted: 9 October 2013
First available in Project Euclid: 11 January 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03AXX 03BXX
Secondary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30} 03B50: Many-valued logic

Self-referential truth Kripke’s theory of truth game-theoretic semantics


Wintein, Stefan. From Closure Games to Strong Kleene Truth. Notre Dame J. Formal Logic 57 (2016), no. 2, 153--179. doi:10.1215/00294527-3346590.

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