A Mystery of Grzegorczyk's Logic of Descriptions

In 2011, Andrzej Grzegorczyk formulated Logic of Descriptions (LD), a new logical system in which the classical equivalence has been replaced with the descriptive equivalence. Two sentences are descriptively equivalent whenever they describe the same state of a?airs. Grzegorczyk's logic LD is built from the ground up by revising the axioms of classical propositional logic and rejecting those that do not correspond to the intended interpreta- tion of the descriptive equivalence as the connective expressing equimeaning relations between sentences. Grzegorczyk's last paper, which introduced in detail philosophical motivations of LD and its axiomatization, has become an inspiration for investigating the properties of LD and its various modi?- cations. In this paper we present the basics of Grzegorczyk's logic LD and then we survey the recent results on LD that have shed light on mysterious properties of the Grzegorczyk's descriptive equivalence connective.