Modeling Belief in Dynamic Systems, Part I: Foundations

TL;DR

This paper introduces a semantic framework for modeling belief change in agents, integrating knowledge, plausibility, and time, and explores how belief can be characterized as a KD45 operator through natural properties.

Contribution

It proposes a general semantic model for belief change based on knowledge and plausibility, extending existing frameworks to include temporal aspects and minimal change via conditioning.

Findings

Belief can be modeled as a KD45 operator under natural properties.

The framework incorporates time, knowledge, and plausibility for dynamic belief modeling.

Conditioning on plausibility measures captures various belief change scenarios.

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 p if he knows that p is more plausible than its negation. 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 revisionand belief update, fit into our framework.