# Repertoire Contraction

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## Abstract

The basic assumption of repertoire contraction is that only some of the logically closed subsets of the original belief set are viable as contraction outcomes. Contraction takes the form of choosing directly among these viable outcomes, rather than among cognitively more far-fetched objects such as possible worlds or maximal consistent subsets of the original belief set. In this first investigation of repertoire contraction, postulates for various variants of the operation are introduced. Necessary and sufficient conditions are given for when repertoire contraction coincides with AGM contraction or with operations generated by AGM-style contraction on a belief base. A close connection is shown to hold between repertoire contraction and specified meet contraction.

## Keywords

Repertoire contraction Outcome set AGM Specified meet contraction Partial meet contraction Full meet contraction Maxichoice contraction Kernel contraction Base-generated operations## Notes

### Acknowledgments

I would like to thank two anonymous referees for unusually detailed and useful comments on an earlier version of this paper.

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