Tim French, Wiebe van der Hoek, Petar Iliev and Barteld Kooi. Succinctness of Epistemic Languages. In: T. Walsh (editor). Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI-11), pp. 881-886, AAAI Press, Menlo Park.

Let be the class of frames satisfying the condition.

We prove that modal logic formulated in a language with the cover modality is exponentially more succinct than the usual box-and-diamond version. In contrast with this, we show that adding the so-called public announcement operator to the latter results in a modal system that is exponentially more succinct than the one based on the cover modality.