DS-2001-04:
Iemhoff, Rosalie
(2001)
*Provability Logic and Admissible Rules.*
Doctoral thesis, University of Amsterdam.

Text (Full Text)
DS-2001-04.text.ps.gz Download (406kB) |

## Abstract

%Nr: DS-2001-04

%Author: Rosalie Iemhoff

%Title: Provability Logic and Admissible Rules

This thesis consists of two parts. In the first part the provability and

preservativity logic of Heyting Arithmetic are studied, and the second part

contains results in intuitionistic propositional logic. The two parts are

connected via admissible rules; they play a central role in the provability

logic of Heyting Arithmetic and are the main topic of the second part of the

thesis.

Up till now there are no axiomatizations known for provability logics of

constructive theories. However, in the first part of the thesis it is shown

that for many well-known properties of Heyting Arithmetic that are

expressible in provability logic, it is known whether they belong to the

logic or not. Therefore, it is argued that the system studied in the thesis

forms at least a very natural fragment, if not all, of the provability logic

of Heyting Arithmetic. The principles of this system are studied from the

modal point of view. Therefore, this part of the thesis can also be viewed

as a study in intuitionistic modal logic, in which surprising frame

properties become visible. It is shown that the given system is complete

with respect to a certain class of frames. The principles are also studied

separately and proved to be independent.

The second part of the thesis is about intuitionistic propositional logic.

First, a basis for the admissible rules of this logic is established. Then

it is shown that intuitionistic propositional logic is characterized by these

rules plus the Disjunction Property. In a similar way it is shown that every

finite part of the basis plus the Disjunction Property characterizes one of

the Gabbay-de Jongh logics. This shows that the characterization of

intuitionistic propositional logic is optimal; no finite part of the basis

characterizes it.

Item Type: | Thesis (Doctoral) |
---|---|

Report Nr: | DS-2001-04 |

Series Name: | ILLC Dissertation (DS) Series |

Year: | 2001 |

Subjects: | Logic |

Depositing User: | Dr Marco Vervoort |

Date Deposited: | 14 Jun 2022 15:16 |

Last Modified: | 14 Jun 2022 15:16 |

URI: | https://eprints.illc.uva.nl/id/eprint/2023 |

## Actions (login required)

View Item |