Modeling beliefs in dynamic systems
The problem of belief change--that is, how beliefs change over time--is a central problem in AI. In this dissertation, we propose a new approach to dealing with belief change. This approach is based on developing a semantics for beliefs. This semantics is embedded in a framework that models agents' knowledge (or information) as well as their beliefs, and how these change in time. We argue, and demonstrate by examples, that this framework can naturally model any dynamic system. Moreover, the framework allows us to consider what the properties of well-behaved belief change should be. 
As we show, such a framework can give us a much deeper understanding of how and why beliefs change. In particular, we can gain a better understanding of the current approaches to belief change--belief revision and belief update. Roughly, revision treats a surprising observation (one that is inconsistent with the agent's current beliefs) as a sign that the beliefs are incorrect, while update treats a surprising observation as an indication that the world has changed. We show how belief revision and belief update can be captured in the proposed framework. This allows us to compare the assumptions made by each method and to better understand the principles underlying them. 
This analysis shows that revision and update are only two points on a spectrum. In general, we would expect that an agent making an observation may both want to revise some earlier beliefs and assume that some change has occurred in the world. We describe a novel approach to belief change that allows us to do this, by applying ideas from probability theory. This approach is based on a qualitative analogue of the Markov assumption, which gives us a well-behaved notion of belief change, without making the occasionally unreasonable assumptions made by belief revision and update. In particular, it allows a user to weigh the relative plausibility that a given observation is due to a change in the world or due to an inaccuracy in previous beliefs.