Going further \({\textsf{LP}}\), and Justification Logic in general, is not only sufficiently refined to distinguish justification assertions for logically equivalent sentences, it provides a flexible machinery to connect justifications of equivalent sentences and hence to maintain constructive closure properties necessary for a quality logic system. For example, let \(X\) and \(Y\) be provably equivalent, i.e., there is a proof \(u\) of \(X\leftrightarrow Y\), and so \(u{:}(X\leftrightarrow Y)\) is provable in \({\textsf{LP}}\). Suppose also that \(v\) is a proof of \(X\), and so \(v{:}X\). It has already been mentioned that this does not mean \(v\) is a proof of \(Y\)—this is a hyperintensional context. However within the framework of Justification Logic, building on the proofs of \(X\) and of \(X\leftrightarrow Y\), we can construct a proof term \(f(u,v)\) which represents the proof of \(Y\) and so \(f(u,v){:}Y\) is provable. In this respect, Justification Logic goes beyond Cresswell’s expectations: logically equivalent sentences display different but constructively controlled epistemic behavior.