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.

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

The Classification of Propositional Calculi

Alexander S. Karpenko
Studia Logica: An International Journal for Symbolic Logic
Vol. 66, No. 2, In Memory of V. A. Smirnov (Nov., 2000), pp. 253-271
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016227
Page Count: 19
  • Download ($43.95)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
The Classification of Propositional Calculi
Preview not available

Abstract

We discuss Smirnov's problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H→ of the intuitionistic propositional logic to an implicational fragment TV→ of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics.

Page Thumbnails

  • Thumbnail: Page 
[253]
    [253]
  • Thumbnail: Page 
254
    254
  • Thumbnail: Page 
255
    255
  • Thumbnail: Page 
256
    256
  • Thumbnail: Page 
257
    257
  • Thumbnail: Page 
258
    258
  • Thumbnail: Page 
259
    259
  • Thumbnail: Page 
260
    260
  • Thumbnail: Page 
261
    261
  • Thumbnail: Page 
262
    262
  • Thumbnail: Page 
263
    263
  • Thumbnail: Page 
264
    264
  • Thumbnail: Page 
265
    265
  • Thumbnail: Page 
266
    266
  • Thumbnail: Page 
267
    267
  • Thumbnail: Page 
268
    268
  • Thumbnail: Page 
269
    269
  • Thumbnail: Page 
270
    270
  • Thumbnail: Page 
271
    271