We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations.

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Epistemic logic investigates what agents know or believe about certain factual descriptions of the world, and about each other. It builds on a model of what information is (statically) available in a given system, and isolates general principles concerning knowledge and belief. The information in a system may well change as a result of various changes: events from the outside, observations by the agents, communication between the agents, etc. This requires information updates. These have been investigated in computer science via interpreted sys-tems; in philosophy and in artificial intelligence their study leads to the area of belief revision. A more recent development is called dynamic epistemic logic. Dynamic epistemic logic is an extension of epistemic logic with dynamic modal operators for belief change (i.e., information update). It is the focus of our contribution, but its relation to other ways to model dynamics will also be discussed in some detail. Situating the chapter This chapter works under the assumption that knowledge is a variety of true justifiable belief. The suggestion that knowledge is nothing but true justified belief is very old in philosophy, going back to Plato if not further. The picture is that we are faced with alternative “worlds”, including perhaps our own world but in addition other

This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take place in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness.

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The combination of logic and game theory provides a fine-grained perspective on information and interaction dynamics, a Theory of Play. In this paper we lay down the main components of such a theory, drawing on recent advances in the logical dynamics of actions, preferences, and information. We then show how this fine-grained perspective has already shed new light on the long-term dynamics of information exchange, as well as on the much-discussed question of extensive game rationality.

This paper provides a sound and complete proof system for a language Le+Y that adds to Dynamic Epistemic Logic (DEL) a discrete previous-time operator as well as single symbol formulas that partially reveal the most recent event that occured. The completeness theorem is by filtration followed by model unravelling and other model transformations. Decidability follows from the completeness proof. The degree to which it is important to include the additional single symbol formulas is addressed in a discussion about the difficulties of the completeness for a language LY that only adds the previous-time operator to DEL. Discussion is also given regarding the completeness for a language obtained by removing common knowledge operators from Le+Y.

We contrast Bonanno’s ‘Belief Revision in a Temporal Framework ’ [15] with preference change and belief revision from the perspective of dynamic epistemic logic (DEL). For that, we extend the logic of communication and change of [11] with relational substitutions [8] for preference change, and show that this does not alter its properties. Next we move to a more constrained context where belief and knowledge can be defined from preferences [29; 14; 5; 7], prove completeness of a very expressive logic of belief revision, and define a mechanism for updating belief revision models using a combination of action priority update [7] and preference substitution [8]. 1 Reconstructing AGM Style Belief Revision Bonanno’s paper offers a rational reconstruction of Alchourrón Gärdenfors Makinson style belief revision (AGM belief revision) [1] (see also [22] and [23]), in a framework where modalities B for single agent belief and I for

Various combinations of temporal logics, epistemic and doxastic logics, and action logics have been used to reason about (groups of) agents in social situations. A key issue that has emerged is how best to represent and reason about the underlying protocol that governs the agents ’ interactions in a particular social situation. In this paper, we propose a PDL-style logic for reasoning about protocols under imperfect information. Our paper touches on a number of issues surrounding the relationship between an agent’s abilities, available choices and information in an interac-tive situation. The main question we address is under what circumstances can the agent commit to a protocol or plan, and what can she achieve by doing so?

We present a coalgebraic semantics for reasoning about information update in multi-agent systems. The novelty is that we have one structure for both states and actions and thus our models do not involve the ”change-of-model” phenomena that arise when using Kripke models. However, we prove that the usual models can be constructed from ours by categorical adjunction. The generality and abstraction of our coalgebraic model turns out to be extremely useful in proving preservation properties of update. In particular, we prove that positive knowledge is preserved and acquired as a result of epistemic update. We also prove common and nested knowledge properties of epistemic updates induced by specific epistemic actions such as public and private announcements, lying, and in particular unsafe actions of security protocols. Our model directly gives rise to a coalgebraic logic with both dynamic and epistemic modalities. We prove a soundness and completeness result for this logic, and illustrate the applicability of the logic by deriving knowledge properties of a simple security protocol.