# Dynamic Epistemic Logic for Implicit and Explicit Beliefs

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## Abstract

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are *logically omniscient*: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit *knowledge*; the present work focuses on acts that affect an agent’s implicit and explicit *beliefs*. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs.

## Keywords

Epistemic logic Dynamic epistemic logic Knowledge Beliefs Belief revision Inference## Notes

### Acknowledgments

The author thanks the organisers and the audiences of the *Workshop on Theories of Information Dynamics and Interaction and their Application to Dialogue (TIDIAD’09)* and the *Third Workshop on Logics for Resource-Bounded Agents (LRBA-3)* as well as the anonymous referees of those workshops and of this special issue; their comments and observations have greatly improved this paper. Special thanks go to the editors of this special issue for all their work and effort. The author also thanks Johan van Benthem for the illuminating ideas that started this project, and Hans van Ditmarsch for pointing out some flaws in old versions and for the many suggestions that have helped to make this work better.

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