Journal of Logic, Language and Information

, Volume 6, Issue 2, pp 123–146

Counterfactuals and Updates as Inverse Modalities

Authors

  • Mark Ryan
    • School of Computer ScienceUniversity of Birmingham
  • Pierre-Yves Schobbens
    • Institut d‘InformatiqueFacultées Universitaires de Namur
Article

DOI: 10.1023/A:1008218502162

Cite this article as:
Ryan, M. & Schobbens, P. Journal of Logic, Language and Information (1997) 6: 123. doi:10.1023/A:1008218502162

Abstract

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 postulatesU1--U8 are translated into counterfactual rules C1--C8(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.

Updatescounterfactualsconditional logicbelief revisioninverse modalitiesmulti-modal logiccorrespondence theoryKripke semantics

Copyright information

© Kluwer Academic Publishers 1997