 Logical equivalence. Sentences \(\psi\) and \(\chi\) of \(\mathbf{IFL}\) are truth equivalent if they are true in precisely the same models, and falsity equivalent if they are false in precisely the same models. Sentences \(\psi\) and \(\chi\) are logically equivalent if they are both truth equivalent and falsity  equivalent.[28]  Due to the failure of bivalence, in \(\mathbf{IFL}\) truth equivalence does not guarantee logical equivalence. 