If you need an accessible version of this item please contact JSTOR User Support

Relevant Implication and the Weak Deduction Theorem

Diderik Batens
Studia Logica: An International Journal for Symbolic Logic
Vol. 46, No. 3 (1987), pp. 239-245
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015314
Page Count: 7
  • Download PDF
  • Cite this Item

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.

If you need an accessible version of this item please contact JSTOR User Support
Relevant Implication and the Weak Deduction Theorem
Preview not available

Abstract

It is shown that the implicational fragment of Anderson and Belnap's R, i.e. Church's weak implicational calculus, is not uniquely characterized by MP (modus ponens), US (uniform substitution), and WDT (Church's weak deduction theorem). It is also shown that no unique logic is characterized by these, but that the addition of further rules results in the implicational fragment of R. A similar result for E is mentioned.

Page Thumbnails

  • Thumbnail: Page 
[239]
    [239]
  • Thumbnail: Page 
240
    240
  • Thumbnail: Page 
241
    241
  • Thumbnail: Page 
242
    242
  • Thumbnail: Page 
243
    243
  • Thumbnail: Page 
244
    244
  • Thumbnail: Page 
245
    245