Abstract
D ynamic epistemic logic as viewed by Baltag, Moss and Solecki (BMS) and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, BMS adds dynamics to epistemic logic by introducing so-called event models as syntactic objects into the language. On the other hand, PDL has instead transition relations between possible worlds. This last approach allows to easily introduce converse events. In this paper we add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that BMS can be translated into EDL thanks to this use of the converse operator : it enables us to translate the structure of the event model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic event model in the language (as done in BMS).We show that EDL is more expressive and general than BMS and we characterize semantically and syntactically in EDL this embedding of BMS.
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Notes
- 1.
EDL is related to Segerberg’s Doxastic Dynamic Logic DDL (Segerberg, 1995, Segerberg, 1999). But research on DDL focusses mainly on its relation with AGM theory of belief revision, and studies particular events of the form + ϕ (expansion by ϕ), * ϕ (revision by ϕ), and − ϕ (contraction by ϕ).
- 2.
Note that we use ⊗ EDL to distinguish our product construction here from the BMS product that we write ⊗ BMS from now on to avoid confusion.
- 3.
- 4.
This notion of weak no miracles is only introduced in our chapter.
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Aucher, G., Herzig, A. (2011). Exploring the Power of Converse Events. In: Girard, P., Roy, O., Marion, M. (eds) Dynamic Formal Epistemology. Synthese Library, vol 351. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0074-1_4
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