Sigma algebras in probabilistic epistemic dynamics

Authors:
Luca Aceto;Wiebe van der Hoek;Anna Ingolfsdottir;Joshua Sack
Affiliations:
Reykjavík University, Reykjavík, Iceland;University of Liverpool, Liverpool, UK;Reykjavík University, Reykjavík, Iceland;Long Beach, California
Venue:
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
Year:
2011

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Abstract

This paper extends probabilistic dynamic epistemic logic from a finite setting to an infinite setting, by introducing σ-algebras to the probability spaces in the models. This may extend the applicability of the logic to a real world setting with infinitely many possible measurements. It is shown that the dynamics preserves desirable properties of measurability and that completeness of the proof system holds with the extended semantics.