A Knowledge-Based Framework for Belief Change. Part I: Foundations
N. Friedman and J. Y. Halpern
In R. Fagin, ed. Theoretical
Aspects of Reasoning about Knowledge: Proc. Fifth Conference (TARK'94).
Morgan Kaufman, San Francisco, CA. 1994. 44-64.
We propose a general framework in which to study belief change.
We begin by defining belief in terms of knowledge and plausibility:
an agent believes $\phi$ if he knows that $\phi$ is true in all the
worlds he considers most plausible. 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
framework of Halpern and Fagin for modeling knowledge
in multi-agent systems. We show that our framework is quite
lets us model in a natural way a number of
different scenarios for belief change.
For example, we show how we can capture an analogue to prior
probabilities, which can be updated by ``conditioning''.
In a related paper, we
show how the two best studied scenarios,
belief revision and belief update, fit into the framework.
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