Bulletin of Symbolic Logic

Explicit Provability and Constructive Semantics

Sergei N. Artemov

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 $\lambda$-calculus.

Article information

Source
Bull. Symbolic Logic, Volume 7, Number 1 (2001), 1-36.

Dates
First available in Project Euclid: 20 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1182353754

Mathematical Reviews number (MathSciNet)
MR1836474

Zentralblatt MATH identifier
0980.03059

JSTOR