Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Counterfactuals and Updates as Inverse Modalities

Mark Ryan and Pierre-Yves Schobbens
Journal of Logic, Language, and Information
Vol. 6, No. 2, Special Issue on Cognitive Actions in Focus (TARK 1996) (Apr., 1997), pp. 123-146
Published by: Springer
Stable URL: http://www.jstor.org/stable/40180100
Page Count: 24
  • Download ($43.95)
  • Cite this Item
Counterfactuals and Updates as Inverse Modalities
Preview not available

Abstract

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.

Page Thumbnails

  • Thumbnail: Page 
123
    123
  • Thumbnail: Page 
124
    124
  • Thumbnail: Page 
125
    125
  • Thumbnail: Page 
126
    126
  • Thumbnail: Page 
127
    127
  • Thumbnail: Page 
128
    128
  • Thumbnail: Page 
129
    129
  • Thumbnail: Page 
130
    130
  • Thumbnail: Page 
131
    131
  • Thumbnail: Page 
132
    132
  • Thumbnail: Page 
133
    133
  • Thumbnail: Page 
134
    134
  • Thumbnail: Page 
135
    135
  • Thumbnail: Page 
136
    136
  • Thumbnail: Page 
137
    137
  • Thumbnail: Page 
138
    138
  • Thumbnail: Page 
139
    139
  • Thumbnail: Page 
140
    140
  • Thumbnail: Page 
141
    141
  • Thumbnail: Page 
142
    142
  • Thumbnail: Page 
143
    143
  • Thumbnail: Page 
144
    144
  • Thumbnail: Page 
145
    145
  • Thumbnail: Page 
146
    146