PP-2006-26: Exploring the iterated update universe

PP-2006-26: Sadzik, Tomasz (2006) Exploring the iterated update universe. [Report]

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Abstract

We investigate the asymptotic properties of the logical system for information update developped by Baltag, Moss and Soleck. We build on the idea of looking at update logics as dynamical systems. We show that every epistemic formula either always holds or is always refuted from certain moment on, in the course of update with factual epistemic events, i.e. events with only propositional prerequisite formulas, or signals. We characterize in terms of a pebble game the class of frames such that iterated update with factual epistemic events built over them gives rise only to finite sets of reachable states. The characterization is nontrivial, and so the 'Finite Evolution Conjecture' is refuted. Finally, after giving some basic insights into the dissipative nature of update with general, nonfactual epistemic events, we show the distinctive stabilizing nature of epistemically ordered multi-S5 events - events in which agents can be ordered in terms of how much they know.

Item Type: Report
Report Nr: PP-2006-26
Series Name: Prepublication (PP) Series
Year: 2006
Uncontrolled Keywords: update
Depositing User: Benedikt
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/201

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