## Explicit Provability And Constructive Semantics (2001)

Venue: | Bulletin of Symbolic Logic |

Citations: | 114 - 22 self |

### BibTeX

@ARTICLE{Artemov01explicitprovability,

author = {Sergei N. Artemov},

title = {Explicit Provability And Constructive Semantics},

journal = {Bulletin of Symbolic Logic},

year = {2001},

volume = {7},

pages = {1--36}

}

### Years of Citing Articles

### OpenURL

### Abstract

In 1933 G odel 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 G odel's provability calculus is nothing but the forgetful projection of LP. This also achieves G odel'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 #-calculus.