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A Qualitative Theory of Dynamic Interactive Belief Revision

  • Alexandru Baltag
  • Sonja Smets
Part of the Springer Graduate Texts in Philosophy book series (SGTP, volume 1)

Abstract

We present a logical setting that incorporates a belief-revision mechanism within Dynamic-Epistemic logic. As the “static” basis for belief revision, we use epistemic plausibility models, together with a modal language based on two epistemic operators: a “knowledge” modality K (the standard S5, fully introspective, notion), and a “safe belief” modality □ (“weak”, non-negatively-introspective, notion, capturing a version of Lehrer’s “indefeasible knowledge”). To deal with “dynamic” belief revision, we introduce action plausibility models, representing various types of “doxastic events”. Action models “act” on state models via a modified update product operation: the “Action-Priority” Update. This is the natural dynamic generalization of AGM revision, giving priority to the incoming information (i.e., to “actions”) over prior beliefs. We completely axiomatize this logic, and show how our update mechanism can “simulate”, in a uniform manner, many different belief-revision policies.

Notes

Acknowledgements

Sonja Smets’ contribution to this research was made possible by the post-doctoral fellowship awarded to her by the Flemish Fund for Scientific Research. We thank Johan van Benthem for his insights and help, and for the illuminating discussions we had with him on the topic of this paper. His pioneering work on dynamic belief revision acted as the “trigger” for our own. We also thank Larry Moss, Hans van Ditmarsch, Jan van Eijck and Hans Rott for their most valuable feedback. Finally, we thank the editors and the anonymous referees of the LOFT7-proceedings for their useful suggestions and comments.

During the republication of this paper in 2015, the research of Sonja Smets was funded by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no.283963.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.ILLCUniversity of AmsterdamAmsterdamThe Netherlands

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