Bridges between dynamic doxastic and doxastic temporal logics

Authors:
Johan Van Benthem;Cédric Dégremont
Affiliations:
Institute of Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands and Department of Philosophy, Stanford University, Stanford, CA;Institute of Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands
Venue:
LOFT'08 Proceedings of the 8th international conference on Logic and the foundations of game and decision theory
Year:
2008

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Abstract

This paper builds bridges between the two main families of modal logics of belief change, both based on plausibility pre-orders: dynamic doxastic logics computing stepwise updates, and temporal doxastic logics describing global system evolutions. Following earlier results linking dynamic-epistemic and epistemic-temporal logics, we prove representation theorems showing under which conditions a doxastic temporal model can be represented as the stepwise evolution of a doxastic model under successive 'priority updates'. This allows for merges, where, in particular, the notion of a 'temporal protocol' defining a global information process (for instance of communication or learning) can be introduced into the more local dynamic perspective.