Title: Update, Probability, Knowledge and Belief

Speaker: Jan van Eijck

Homepage: http://homepages.cwi.nl/~jve/

Date:  15:10-18:00, 22th, Oct.

Location: Romm B114, Building 2, Philosophy Department, Li Zhaoji Humanites Garden, Peking University

                 北大李兆基人文学苑哲学系2号楼B114（地下）

Abstract: The talk will trace various connections between update, probability, knowledge and belief. In one direction, one may start with probability, and next relate knowledge to certainty, strength of belief to willingness to bet, and update to (Bayesian) conditionalization. In another direction, one may start from knowledge, belief and public announcement, and next derive probability from an appropriate strengthening of these notions. A third possibility is to start out from a system that has knowledge and probability combined. For this, we will present a simplified version of probabilistic epistemic logic. We will define epistemic weight models with updates, and show how these can serve as a basis for a simplification of the logic of probabilistic dynamic epistemic updates. We will demonstrate the virtues of this third approach by showing how it can be used for probabilistic epistemic model checking in the tool PRODEMO. This brief demonstration with PRODEMO, our prototype model checker for probabilistic epistemic logic, will hopefully convince you that update by public announcement and update by Bayesian conditioning are two sides of the same coin. Further issues that we will address are the distinction between risk and uncertainty, and the analysis of the concept of bias (or: unknown probability).  In this context, we will discuss the postconditions of protocols that are designed to eliminate bias, such as the well-known Von Neumann protocol to simulate a fair coin with a biased one. If there is time, we will also reflect on a further issue of considerable importance concerning the notion of bias: how does one recognize one's own bias, and if possible, eliminate it?