Besides the disquotational feature of truth, one would also like to capture the compositional features of truth and generalize the axioms of typed compositional truth to the type-free case. To this end, axioms or rules concerning the truth of atomic sentences with the truth predicate will have to be added and the restriction to \(T\)-free sentences in the compositional axioms will have to be lifted. In order to treat truth like other predicates, one will add the axiom \(\forall{\scriptsize A}(T[T{\scriptsize A}] \leftrightarrow T{\scriptsize A})\) (where \(\forall{\scriptsize A}\) ranges over all sentences). If the type restriction of the typed compositional axiom for negation is removed, the axiom \(\forall{\scriptsize A}(T[\neg{\scriptsize A}] \leftrightarrow \neg T{\scriptsize A})\) is obtained.