Cluster expansion and the boxdot conjecture
Emil Jeřábek · Mathematical logic quarterly · 2016
The boxdot conjecture asserts that every normal modal logic that faithfully interprets by the well-known boxdot translation is in fact included in . We confirm that the conjecture is true. More generally, we present a simple semantic condition on modal logics L0 which ensures that the largest logic where L0 embeds faithfully by the boxdot translation is L0 itself. In particular, this natural generalization of the boxdot conjecture holds for , , and in place of .