Speaker: Dominik Klein (University of Bayreuth)
Date and Time: Thursday, February 22nd 2018, 16:00-17:30
Venue: KdVI Seminar Room F3.20, Science Park 107.
Title: In the Long Run we’re all Dead: On Kripke Models, Iterated Updates and Dynamic Systems.
Abstract. In this talk, we explore the universe of iterated product updates. The talk has two main components. In the first part, we show how iterated product updates can be understood as a dynamic system. In particular, we equip the space of Kripke models with a metric and prove the resulting topology compact. We then show that product updates are continuous with respect to this metric, allowing to understand iterated updates as a discrete time dynamical systems.
In the second part of the talk, we apply this apparatus to the case of iterated updates with one and the same event model. There, we expand on a result by Sadzik (2006) that answered a hypothesis by Johan van Benthem to the negative. Sadzik showed that there are pairs of a Kripke Model M and an event model E, such that the process of repeatedly updating M with E never stabilizes nor becomes cyclic. Using our metric based apparatus, we show that Sadzik’s example does, however, stabilize in the infinite, i.e. that the sequence converges to a unique limit point. In fact, we determine a set of conditions on E, the event model, under which iterated update converges in the limit. Finally, we show that Sadzik’s result has an infinite counterpart: There are event models E that, when iteratedly applied to a suitable Kripke model M, display nontrivial limit behavior. They do not converge to a single point nor a limit cycle in the infinite. This is joint work with Rasmus Rendsvig.