# Modeling Beliefs in Dynamic Systems. Part I: Foundations

## N. Friedman and J. Y. Halpern

To appear in Artificial Intelligence.

Earlier version appeared under the title A Knowledge-Based Framework for Belief Change. Part I: Foundations in R. Fagin, ed. Theoretical Aspects of Reasoning about Knowledge: Proc. Fifth Conference (TARK'94). Morgan Kaufman, San Francisco, CA. 1994. 44-64.

### Abstract

Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better understanding of belief change can be gained from examining appropriate semantic models. In this paper we propose a general framework in which to model belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes $\phi$ if he knows that $\phi$ is more plausible than $\neg\phi$. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin for modeling knowledge in multi-agent systems. We then examine the problem of minimal change''. This notion can be captured by using prior plausibilities, an analogue to prior probabilities, which can be updated by conditioning''. We show by example that conditioning on a plausibility measure can capture many scenarios of interest. In a companion paper, we show how the two best-studied scenarios of belief change, {\em belief revision and belief update, fit into our framework.

nir@cs.huji.ac.il