Counterfactuals and Updates as Inverse Modalities

  • Authors:

  • Mark Ryan;Pierre-Yves Schobbens

  • Affiliations:

  • School of Computer Science, University of Birmingham, Birmingham B15 2TT, U.K. (E-mail: mdr@cs.bham.ac.uk, http://www.cs.bham.ac.uk/˜mdr);Institut d‘Informatique, Facultées Universitaires de Namur, Rue Grandgagnage 21, 5000 Namur, Belgium (E-mail: pys@info.fundp.ac.be, http://www.info.fundp.ac.be/˜pys)

  • Venue:
  • Journal of Logic, Language and Information
  • Year:
  • 1997

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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.