# Announcements to Attentive Agents

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## Abstract

In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief.

## Keywords

Dynamic epistemic logic Axiomatization Satisfiability Common belief Collective attention## Notes

### Acknowledgments

Hans van Ditmarsch is also affiliated to IMSc, Chennai, as research associate. We acknowledge support from European Research Council Grant EPS 313360. Andreas Herzig and Emiliano Lorini acknowledge support of the the ANR project EmoTES. We gratefully acknowledge two very informed and helpful reviewers of JoLLI. This work is based on a conference publication van Ditmarsch et al. (2013). All parts have been thoroughly revised. The section on attention change has been expanded considerably. A completely novel addition is the section on common belief and the axiomatization for that extension.

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