We present a direct reduction of dynamic epistemic logic in the spirit of [4] to propositional dynamic logic (PDL) [17, 18] by program transformation. The program transformation approach associates with every update action a transformation on PDL programs. These transformations are then employed in reduction axioms for the update actions. It follows that the logic of public announcement, the logic of group announcements, the logic of secret message passing, and so on, can all be viewed as subsystems of PDL. Moreover, the program transformation approach can be used to generate the appropriate reduction axioms for these logics. Our direct reduction of dynamic epistemic logic to PDL was inspired by the reduction of dynamic epistemic logic to automata PDL of [13]. Our approach shows how the detour through automata can be avoided. 1

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions regarding common knowledge express the essence of what communication achieves. We present some methods that yield so-called reduction axioms for common knowledge. We investigate the expressive power of public announcement logic with relativized common knowledge, and present reduction axioms that give a detailed account of the dynamics of common knowledge in some major communication types.

Dynamic logic, broadly conceived, is the logic that analyses change by decomposing actions into their basic building blocks and by describing the results of performing actions in given states of the world. The actions studied by dynamic logic can be of various kinds: actions on the memory state of a computer, actions of a moving robot in a closed world, interactions between cognitive agents performing given communication protocols, actions that change the common ground between speaker and hearer in a conversation, actions that change the contextually available referents in a conversation, and so on. In each of these application areas, dynamic logics can be used to model the states involved and the transitions that occur between them. Dynamic logic is a tool for both state description and action description. Formulae describe states, while actions or programs express state change. The levels of state descriptions and transition characterisations are connected by suitable operations that allow reasoning about pre- and postconditions of particular changes.

Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also show how such systems can deal with factual alteration, rather than just information change, making them cover a much wider range of realistic events. After a warm-up stage of analyzing logics for public announcements, our main technical results are expressivity and completeness theorems for a much richer logic that we call LCC. This is a dynamic epistemic logic whose static base is propositional dynamic logic (PDL), interpreted epistemically. This system is capable of expressing all modelshifting operations with finite action models, while providing a compositional analysis for a wide range of informational events. This makes LCC a serious candidate for a standard in dynamic epistemic logic, as we illustrate by analyzing some complex communication scenarios, including sending successive emails with both ‘cc’ and ‘bcc ’ lines, and other private announcements to subgroups. Our proofs involve standard modal techniques, combined with a new application of Kleene’s Theorem on finite automata, as well as new Ehrenfeucht games of model comparison.

Abstract. We investigate the asymptotic properties of the logical system for information update developped by Baltag, Moss and Solecki [2]. We build on the idea of looking at update logics as dynamical systems. We show that every epistemic formula either always holds or is always refuted from certain moment on, in the course of update with factual epistemic events, i.e. events with only propositional prerequisite formulas, or signals. We characterize in terms of a pebble game the class of frames such that iterated update with factual epistemic events built over them gives rise only to finite sets of reachable states. The characterization is nontrivial, and so the ’Finite Evolution Conjecture ’ (see van Benthem [4]) is refuted. Finally, after giving some basic insights into the dissipative nature of update with general, nonfactual epistemic events, we show the distinctive stabilizing nature of epistemically ordered multi-S5 events- events in which agents can be ordered in terms of how much they know. 1.