In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic 9. College Publications. pp. 348-367 (2012)

Authors
Thomas Icard
Stanford University
Wesley H. Holliday
University of California, Berkeley
Abstract
Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PAL-K_omega, as well as standard extensions thereof, e.g., PAL-T_omega, PAL-S4_omega, and PAL-S5_omega. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.
Keywords dynamic epistemic logic  Public Announcement Logic  schematic validity  substitution core  uniform substitution
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References found in this work BETA

Dynamic Epistemic Logic.Hans van Ditmarsch, Wiebe van der Hoek & Barteld Kooi - 2016 - Internet Encyclopedia of Philosophy.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Logics of Public Communications.Jan Plaza - 2007 - Synthese 158 (2):165 - 179.

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