Dynamic Update with Probabilities

Abstract

Abstract.Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods.

A Qualitative Theory of Dynamic Interactive Belief Revision

“…An action plausibility model 16 (APM, for short) is a plausibility frame (Σ, ≤ a ) a∈A together with a precondition map pre : Σ → Prop, associating to each element of Σ some doxastic proposition pre σ . We call the elements of Σ (basic) doxastic actions (or "events"), and we call pre σ the precondition of action σ.…”

“…DEL originates in the work of Gerbrandy and Groeneveld [29,28], anticipated by Plaza in [43], and further developed by numerous authors [6,30,21,4,22,38,5,15,16] etc. In its standard incarnation, as presented e.g.…”

Johan van Benthem on Logic and Information Dynamics

“…Kooi's setting was later extended by van Benthem [60] by decisively enriching event models with occurrence probabilities (a probabilistic version of the usual notion of precondition of an action). A full-fledged Probabilistic Dynamic Epistemic Logic, obtained by adding to the above setting observation probabilities (as a probabilistic version of the doxastic accessibility relations on events in standard DEL), was developed by van Benthem et al [93], and was later extended to infinite models by Sack [187].…”

Epistemic Logic and Information Update

“…A logic that extends the logic of epistemic actions by allowing for factual change and by closing epistemic modalities under regular operations is axiomatized in [102]. A probabilistic version of the action model framework is presented by van Benthem, Gerbrandy and Kooi in [99]. For a more extensive and up-to-date presentation of dynamic epistemic logic (apart from the present contribution), see the textbook 'Dynamic Epistemic Logic' by van Ditmarsch, van der Hoek, and Kooi [113].…”