 Beall’s 2009 theory allows a fully transparent truth predicate: one such that for any sentence \(A\), \(Tr\langle A\rangle\) and \(A\) can be replaced with each other in all (non-opaque) contexts salva veritate, that is, producing sentences logically equivalent to the sentences one started with. Then the unrestricted T-schema follows from transparency (and the fact that \(A \rightarrow A\) is a logical truth) as a special case. In Beall’s theory, all sentences \(A\) that are dialetheias are not only true and false, i.e. (given that falsity is truth of negation), \(Tr\langle A\rangle \wedge Tr\langle \neg A\rangle\); they are also true and untrue, \(Tr\langle A\rangle \wedge \neg Tr\langle A\rangle\): this again follows from the transparency of truth. Beall’s theory is based on a (relevant) paraconsistent logic, whose modal semantics employs so-called  non-normal worlds.  