 Kripke’s construction fits into the fixed point theorem above in the following way. First note that the set of partially interpreted languages that only differ on the interpretation of \(T\) forms a ccpo: Simply define the ordering on these languages by \(L_1 \le L_2\) iff the interpretation of \(T\) in \(L_2\) extends the interpretation of \(T\) in \(L_1\) (that is, the extension and anti-extension of \(T\) in \(L_1\) are included in those of \(L_2)\). Then define a truth revision operator \(\tau\) on these languages by: