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.
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