Abstract
This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the result of, indeed, public announcements. One crucial topic in that setting is that of unsuccessful updates: formulas that become false when announced. The Moore-sentences that were already extensively discussed at the conception of epistemic logic in [15] give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates. Our closing observations are on recent developments that link the ‘standard’ topic of (theory) belief revision [1] to the dynamic epistemic logics introduced here.
This contribution is a reprint of [39], with the exception of some added footnotes and the final section on recent developments that has been thoroughly revised. References have been updated. At the time, Jaakko Hintikka kindly gave permission to use his name in the title. He also observed that “My late wife Merrill was one of the best female blackjack players in the world and a championship level bridge player. Hence twenty years ago you would have been well advised to specify which Hintikka you refer to in your title!” And that was more than 10 years ago... It was a real pleasure for Hans van Ditmarsch to renew his acquaintance with Jaakko Hintikka at a delightful workshop in 2011 in Granada organized by María José Frápolli. At the current occasion we wish to dedicate this contribution to his memory.
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Notes
- 1.
The characterization of successful single-agent formulas has by now been achieved in [16], but for the multi-agent case the question remains open.
- 2.
By now, the approach involving action models has become the main approach in the community—as it already was in 2005 but at that time not yet so in the perception of the authors. They told that story in better perspective in [40]. The action model approach is intuitively very elegant and there are more theoretical results. A well-known treatment within a PDL framework is [31]. The precise relation between these approaches remains unclear, e.g., on the class of S5 models it seems likely that the logics are equally expressive but this is not proved. And in the mean time, there are yet other general approaches to logical dynamics, such as the arrow update logic presented in [18].
- 3.
In action model logic the action of showing a card is modelled by an action model consisting of three alternative actions, with respective preconditions \({\, Clubs}_a\), \({ Hearts}_a\), and \({ Spades}_a\), that can be distinguished from one another by agents a, b but not by agent c; and such that the distinguished action (what really happened, the one having the exclamation mark in the relational approach), is the one with precondition \({\, Clubs}_a\).
- 4.
An exception partially dealing with higher-order belief change in DDL is [19].
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van Ditmarsch, H., van der Hoek, W., Kooi, B. (2018). Playing Cards with Hintikka: An Introduction to Dynamic Epistemic Logic. In: van Ditmarsch, H., Sandu, G. (eds) Jaakko Hintikka on Knowledge and Game-Theoretical Semantics. Outstanding Contributions to Logic, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-62864-6_9
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