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

Explicit Provability and Constructive Semantics

Sergei N. Artemov
The Bulletin of Symbolic Logic
Vol. 7, No. 1 (Mar., 2001), pp. 1-36
DOI: 10.2307/2687821
Stable URL: http://www.jstor.org/stable/2687821
Page Count: 36
  • 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
Explicit Provability and Constructive Semantics
Preview not available

Abstract

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus.

Page Thumbnails

  • Thumbnail: Page 
1
    1
  • Thumbnail: Page 
2
    2
  • Thumbnail: Page 
3
    3
  • Thumbnail: Page 
4
    4
  • Thumbnail: Page 
5
    5
  • Thumbnail: Page 
6
    6
  • Thumbnail: Page 
7
    7
  • Thumbnail: Page 
8
    8
  • Thumbnail: Page 
9
    9
  • Thumbnail: Page 
10
    10
  • Thumbnail: Page 
11
    11
  • Thumbnail: Page 
12
    12
  • Thumbnail: Page 
13
    13
  • Thumbnail: Page 
14
    14
  • Thumbnail: Page 
15
    15
  • Thumbnail: Page 
16
    16
  • Thumbnail: Page 
17
    17
  • Thumbnail: Page 
18
    18
  • Thumbnail: Page 
19
    19
  • Thumbnail: Page 
20
    20
  • Thumbnail: Page 
21
    21
  • Thumbnail: Page 
22
    22
  • Thumbnail: Page 
23
    23
  • Thumbnail: Page 
24
    24
  • Thumbnail: Page 
25
    25
  • Thumbnail: Page 
26
    26
  • Thumbnail: Page 
27
    27
  • Thumbnail: Page 
28
    28
  • Thumbnail: Page 
29
    29
  • Thumbnail: Page 
30
    30
  • Thumbnail: Page 
31
    31
  • Thumbnail: Page 
32
    32
  • Thumbnail: Page 
33
    33
  • Thumbnail: Page 
34
    34
  • Thumbnail: Page 
35
    35
  • Thumbnail: Page 
36
    36