Meaning, shifts and conditioning
Jan‐Willem Romeijn · University of Groningen research database (University of Groningen / Centre for Information Technology) · 2009
This paper investigates the viability of the Bayesian model of belief change. Van Benthem (2003) has shown that a particular kind of information change cannot be modelled by Bayesian conditioning. I argue that the problems come about because the information change alters the semantics in which the change is supposed to be modelled by conditioning: it induces a shift in meanings. I then show that meaning shifts can be modelled as conditioning by employing a semantics that allows to make these changes in meaning explicit, and that the appropriate probability kinematics can be described by Dempster’s rule. 1 Conditioning and meaning shifts In the Bayesian model of belief change, beliefs over sentences, like s and r, are represented with probability assignments over an algebra of propositions, S and R, which are associated with the sentences by an interpretation: a propositions fixes the meaning of a sentence. A belief change due to the acceptance of a sentence is reflected in the probability assignment by conditioning the assignment on the proposition associated with the sentence, as determined by Bayes’ rule,