Counterfactuals and updates as Inverse Modalities

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We point out a simple but hitherto ignored link between the theory of updates, the theory of counterfactuals, and classical modal logic: update is a classical existential modality, counterfactual is a classical universal modality, and the accessibility relations corresponding to these modalities are inverses. The Ramsey Rule (often thought esoteric) is simply an axiomatisation of this inverse relationship. We use this fact to translate between rules for updates and rules for counterfactuals. Thus, Katsuno/Mendelzon's postulates are translated into counterfactual rules, and many of the familiar counterfactual rules are translated into rules for updates. An open question is whether all rules for updates may be translated into rules for counterfactuals, and vice versa. We present a syntactic condition which is sufficient to guarantee that a translation from update to counterfactual (or vice versa) is possible.
Original languageEnglish
Pages (from-to)123-146
Number of pages24
JournalJournal of Logic, Language and Information
Issue number2
Publication statusPublished - 1997


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