A proof-theoretical perspective on Public Announcement Logic

Public Announcement Logic (PAL) is one of the most prominent approaches to the logic of communication and it is concerned with the problem of how a group of agents gains knowledge by announcing to each other certain facts. Since its origin in the work of Plaza (1989) and Gerbrandy and Groenveled (1997), the debate was on whether announcements are assumed to be true or not. In both of cases, the standard proof system for PAL consists in a suitable extension of a Hilbert system for the modal logic S5 and it is of little use for the actual finding of proofs. In this paper a sequent calculus for PAL (G3PAL) is presented and proved to be equivalent to the axiomatic system and thereby complete with respect to the semantics in which any formula can be announced, regardless its truth value; moreover, the cut-elimination theorem makes it possible to find derivations in PAL.