A Semantic-Modal View on Ramsey's Test

Authors
Sonja Smets
University of Amsterdam
Alexandru Baltag
University of Amsterdam
Abstract
We present a semantic analysis of the Ramsey test, pointing out its deep underlying flaw: the tension between the “static” nature of AGM revision (which was originally tailored for revision of only purely ontic beliefs, and can be applied to higher-order beliefs only if given a “backwards-looking” interpretation) and the fact that, semantically speaking, any Ramsey conditional must be a modal operator (more precisely, a dynamic-epistemic one). Thus, a belief about a Ramsey conditional is in fact a higher-order belief, hence the AGM revision postulates are not applicable to it, except in their “backwards-looking” interpretation. But that interpretation is consistent only with a restricted (weak) version of Ramsey’s test (in-applicable to already revised theories). The solution out of the conundrum is twofold: either accept only the weak Ramsey test; or replace the AGM revision operator ∗ by a truly “dynamic” revision operator ⊗, which will not satisfy the AGM axioms, but will do something better: it will “keep up with reality”, correctly describing revision with higher-order beliefs
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