KF is intended to be an axiomatization of Kripke’s (1975) semantical theory. This theory is based on partial logic with the Strong Kleene evaluation scheme. In Strong Kleene logic not every sentence \(\phi \vee \neg \phi\) is a theorem; in particular, this disjunction is not true if \(\phi\) lacks a truth value. Consequently \(T\ulcorner L\vee \neg L\urcorner\) (where \(L\) is the Liar sentence) is not a theorem of KF and its negation is even provable. Cantini (1990) has proposed a system VF that is inspired by the supervaluations scheme. In VF all classical tautologies are provably true and \(T\ulcorner L \vee \neg L\urcorner\), for instance, is a theorem of VF. VF can be formulated in \(\mathcal{L}_T\) and uses classical logic. It is no longer a compositional theory of truth, for the following is not a theorem of VF: