Counterfactuals and Updates as Inverse Modalities
Mark Dermot Ryan, Pierre‐Yves Schobbens, Odinaldo Rodrigues · 1996
. We point out a simple but hitherto ignored link between the theory of updates and 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 postulates for updates and postulates for counterfactuals. Thus, Katsuno/Mendelzon's postulates U1--U8 are translated into counterfactual postulates C1--C8 (table VII), and many of the familiar counterfactual postulates are translated into postulates for updates (table VIII). Our conclusions are summarised in table V. We also present a syntactic condition which is sufficient to guarantee that a translation from update to counterfactual (or vice versa) is possible. 1. Introduction Background. An intuitive connection between theory change and counterfactuals...