On the Infinitely Many-Valued Threshold Logics and von Wright's System M″

✍ Scribed by Akira Nakamura

• Publisher: John Wiley and Sons
• Year: 1962
• Tongue: English
• Weight: 630 KB
• Volume: 8
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19620080207

✦ Synopsis

ON THE INFINITELY MANY-VALUED THRESHOLD LOGICS AND VON WRIGHT'S SYSTEM M" by AKIRA NAKAMURA in Tokyo (Japan) 8 1. Introduction * z z , *is'\ *23, .) 1 1 1 ( * I j " 2 , * 3 , . . .)' = (*I, *a, * 3 , . . .) where LJ, n , Now, we shall give here some definitions in the same way as in [l]. At the first we consider functions f (t) , g ( t ) , . . . with one variable whose domain is arbitrary means the join, the meet and the complement respectively. According to VON WRIQHT [3], M" is equivalent to LEWIS'S system S 5. 2, The author wishes to thank Prof. Dr. M. ITOR who has made valuable suggestions. 10* ~ ~ . l) We notice that this operation T, has concerns with Smln in 2, Strictly speaking, P,Q, . . .,PI, P,, . . . are an interpretation of propositions.

3. Generally, in this definition the occurrence order of P, and the position of parentheses can be arbitrary. This is easily provable in our axiomatic system. Accordingly, in such a case we promise that the occurrence order of Pt and the position of parentheses are determined in a certain way.