Consistent theories of truth for languages which conform to classical logic

Abstract

Every language which conforms to classical logic is shown to have an extension for which a consistent definitional theory of truth is formulated. Also, a consistent semantical theory of truth is formulated for that extension if every sentence of the
object language is valuated by its meaning either as true or as false. These theories of truth contain both a truth predicate and a non-truth predicate. The case where they compose with predicates having several free variables is also included. Theories are equivalent when sentences of the object language are valuated by their meanings.