 The closed-off Kripke construction can help fill in the idea of a determinately operator discussed in  §4.1.3.  Instead of an operator, it allows us to define a predicate \(D(\left\ulcorner A\right\urcorner)\) by \(\Tr(\left\ulcorner A\right\urcorner) \vee \Tr(\left\ulcorner \neg A\right\urcorner). D\) represents ‘determinately’ in the sense of applying to sentences that have a truth value according to \(\Tr\), as it were, ‘determined’ by the model produced by the Kripke construction. It also, as we observed, applies to all the sentences which are well-behaved in the sense of obeying the T-schema (or capture and release).