Now Playing: COUNTERFACTUALS WEEK
Topic: Counterfactuals
Counterfactuals and Updates as Inverse Modalities
By Mark Ryan and Pierre-Yves Schobbens
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 and Mendelzon?s postulates U1--U8 are translated into counterfactual rules C1--C8 (Table VII), and many of the familiar counterfactual rules are translated into rules for updates (Table VIII). Our conclusions are summarised in Table V.
From known properties of inverse modalities we deduce that not 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.
Posted by Tony Marmo
at 00:01 GMT
Updated: Sunday, 4 December 2005 07:09 GMT
