The identity connective is usually interpreted in non-Fregean logic as an operator representing the identity of situations. This interpretation is related to the modal criterion of the identity of sentence correlates, characteristic of the WT system and some stronger systems. However, this connective can also be interpreted in a different way – as an operator representing the identity of propositions. The “propositional” interpretation is in turn associated with the modal-contents criterion of the identity of sentence correlates. This begs the question (...) of whether there is a system of non-Fregean logic, providing an adequate formalization of this criterion. The aim of the paper is to systematize the metalogical and philosophical context of the issue and to point to a system that provides its solution. (shrink)