From DEL to EDL: Exploring the Power of Converse Events

Authors:
Guillaume Aucher;Andreas Herzig
Affiliations:
University of Otago (NZ) - University Paul Sabatier (F) IRIT, Université Paul Sabatier, Toulouse Cedex (F), 31062;University of Otago (NZ) - University Paul Sabatier (F) IRIT, Université Paul Sabatier, Toulouse Cedex (F), 31062
Venue:
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2007

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Abstract

Dynamic epistemic logic (DEL) as viewed by Baltag et col. and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, DELadds dynamics to epistemic logic by introducing so-called epistemic action models as syntactic objects into the language. On the other hand, PDLhas instead transition relations between possible worlds. This last approach allows to easily introduce converse events. We add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that DELcan be translated into EDLthanks to this use of the converse operator: this device enables us to translate the structure of the action (or event) model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic action (event) model in the language (as done in DEL). It follows that EDLis more expressive and general than DEL.