### Distance Semantics for Belief Revision

Daniel Lehmann, Menachem Magidor, and Karl Schlechta
Source: J. Symbolic Logic Volume 66, Issue 1 (2001), 295-317.

#### Abstract

A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula $\alpha$ as the theory defined by the set of all those models of $\alpha$ that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.

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