  The RTT is a clear example of a semantically motivated theory of truth. Quite a different tradition seeks to give a satisfying axiomatic theory of truth. Granted we cannot retain all of classical logic and all of our intuitive principles regarding truth, especially if we allow vicious self-reference. But maybe we can arrive at satisfying axiom systems for truth, that, for example, maintain consistency and classical logic, but give up only a little bit when it comes to our intuitive principles concerning truth, such as the T-biconditionals (interpreted classically); or maintain consistency and all of the T-biconditionals, but give up only a little bit of classical logic. Halbach 2011 comprehensively studies such axiomatic theories (mainly those that retain classical logic), and Horsten 2011 is in the same tradition. Both Chapter 14 of Halbach 2011 and Chapter 8 of Horsten 2011 study the relationship between the Friedman-Sheard theory FS and the revision semantics, with some interesting results. For more work on axiomatic systems and the RTT, see Horsten et al 2012.