Journal of Logic, Language and Information
, Volume 6, Issue 2, pp 123146
First online:
Counterfactuals and Updates as Inverse Modalities
 Mark RyanAffiliated withSchool of Computer Science, University of Birmingham
 , PierreYves SchobbensAffiliated withInstitut d‘Informatique, Facultées Universitaires de Namur
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We point out a simple but hitherto ignored link between the theoryof updates, the theory of counterfactuals, and classical modal logic: update is a classicalexistential modality, counterfactual is a classical universalmodality, 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 andrules for counterfactuals. Thus, Katsuno and Mendelzon‘s postulatesU1U8 are translated into counterfactual rules C1C8(Table VII), and many of the familiar counterfactual rulesare translated into rules for updates (Table VIII). Ourconclusions are summarised in Table V.
From known properties of inverse modalities we deduce that notall rules for updates may be translatedinto rules for counterfactuals, and vice versa. We present asyntactic condition which is sufficient to guarantee that atranslation from update to counterfactual (or vice versa) is possible.
 Title
 Counterfactuals and Updates as Inverse Modalities
 Journal

Journal of Logic, Language and Information
Volume 6, Issue 2 , pp 123146
 Cover Date
 199704
 DOI
 10.1023/A:1008218502162
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Updates
 counterfactuals
 conditional logic
 belief revision
 inverse modalities
 multimodal logic
 correspondence theory
 Kripke semantics
 Authors

 Mark Ryan ^{(1)}
 PierreYves Schobbens ^{(2)}
 Author Affiliations

 1. School of Computer Science, University of Birmingham, Birmingham, B15 2TT, U.K.
 2. Institut d‘Informatique, Facultées Universitaires de Namur, Rue Grandgagnage 21, 5000, Namur, Belgium (Email