The aim of this paper is to give a certain algebraic account of truth: we want to define what we mean by De Morgan-valued truth models and show their existence even in the case of semantical closure: that is, languages may contain their own truth predicate if they are interpreted by De Morgan-valued models. Before we can prove this result, we have to repeat some basic facts concerning De Morgan-valued models in general, and we will introduce a notion of truth both on the object- and on the metalanguage level appropriate for such models. The definitions and the existence theorem are extensions of Kripke's, Woodruff's, and Visser's concepts and results concerning three- and four-valued truth models.
"Truth and the Liar in De Morgan-Valued Models." Notre Dame J. Formal Logic 40 (4) 496 - 514, Fall 1999. https://doi.org/10.1305/ndjfl/1012429715