Elsevier

Artificial Intelligence

Volume 95, Issue 2, September 1997, Pages 257-316
Artificial Intelligence

Modeling belief in dynamic systems, part I: Foundations

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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 Φ if he knows that Φ is more plausible than ¬Φ. 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, belief revision and belief update, fit into our framework.

Keywords

Belief change
Belief revision
Milimal change
Logic of knowledge
Logic of belief
Logic of time
Plausibility measure
AGM postulates

Cited by (0)

Some of this work was done while both authors were at the IBM Almaden Research Center. The first author was also at Stanford while much of the work was done. IBM and Stanford's support are gratefully acknowledged. The work was also supported in part by the Air Force Office of Scientific Research (AFSC), under Contract F49620-91-C-0080 and grant F94620-96-1-0323 and by NSF under grants IRI-95-03109 and IRI-96-25901. A preliminary version of this paper appears in Proceedings of the 5th Conference on Theoretical Aspects of Reasoning About Knowledge (1994) pp. 44–64, under the title “A knowledge-based framework for belief change. Part I: Foundations”.