We show that Booth et al.'s Horn contraction based on infra-remainder sets corresponds exactly to kernel contraction for belief sets. This result is obtained via a detour through Horn contraction for belief bases, which supports the conjecture that Horn belief change is best viewed as a "hybrid" version of belief set change and belief base change. Moreover, the link with base contraction gives us a more elegant representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.
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