 There is an important strand of work in proof theory, which has sought to develop axiomatic theories of self-applicative truth in classical logic, including work of Cantini (1996), Feferman (1984, 1991), Friedman and Sheard (1987), Halbach (2011), and Horsten (2011). The idea is to find ways of expressing rules like capture and release that retain consistency. Options include more care about how proof-theoretic rules of inference are formulated, and more care about formulating restricted rules. The main ideas are discussed in the entry on  axiomatic theories of truth,  to which we will leave the details.