Axiomatic theories of truth take truth as an undefined primitive predicate and aim to axiomatically characterize it. If the truth predicate can operate on sentences (or other truth-bearers) involving the truth predicate itself, then it is called self-applicable (or type-free). Because of the Liar paradox, the naive axiomatization of self-applicable truth is inconsistent, and a variety of restrictions of the naive axioms have been proposed, which result in a plethora of theories of truth. Most of those theories abandon the classical bivalent notion of truth and instead adopt a non-classical notion of truth. However, this move to non-classical truth cripples some important logico-linguistic functions of truth and seems to pose a considerable limitation on the applicability of truth in philosophy and other areas. In this talk, Fujimoto presents a new type of theory of truth that is self-applicable, thoroughly classical, mathematically sound, and with rich mathematical consequences. The main part of this talk is a joint work with Volker Halbach.