Field (2008) and others criticised theories based on partial logic for the absence of a ‘proper’ conditional and bi-conditional. Various authors have proposed conditionals and bi-conditionals that are not definable in terms of \(\neg , \vee\) and \(\wedge\). Field (2008) aims at an axiomatic theory of truth not dissimilar to PKF but with a new conditional. Feferman (1984) also introduced a bi-conditional to a theory in non-classical logic. Unlike Field’s and his own 1984 theory, Feferman’s (2008) theory DT is formulated in classical logic, but it’s internal logic is again a partial logic with a strong conditional.