DS-1995-02:
Prijatelj, Andreja
(1995)
*Investigating Bounded Contraction.*
Doctoral thesis, University of Amsterdam.

## Abstract

The thesis is a collection of four self-contained papers investigating

meta-properties of intuitionistic and classical Gentzen systems with bounded

contraction and their algebraic models.

Two versions of bouded contraction are considered, differing in the restriction

imposed on the usual contraction rule:

s-contraction, where contraction is restricted to a certain basic type

(or equivalently, atomic formula);

n-contraction, for n greater or equal 2, where (n+1)occurrences of a

formula may be contracted to n occurrences.

Substituting s-contraction or n-contraction for full contraction in Gentzen

systems already results in splitting of connectives familiar from linear logic.

Thus particular fragments of intuitionistic and classical linear logic extended with bounded contraction and their affine extensions are explored throughout

this work. There is, however a crucial distinction between the two versions of

contraction from the proof theoretical point of view. Linear systems with

s-contraction retain the cut-elimination property as opposed to those with

n-contraction.

As a result this work can naturally be divided into:

proof theoretical part I, and

algebraic parts II, III, and IV.

The papers collected in this thesis are the following:

(I) Lambek Calculus with Restricted Contraction and Expansion, 1992,

Studia Logica 51, 125-143.

(II) Bounded Contraction and Gentzen-style Formulation of Lukasiewicz Logics,

to appear in Studia Logica.

(III) Connectification for n-Contraction, to appear in Studia Logica.

(IV) Free Algebras Corresponding to Multiplicative Classical Linear Logic and

some Extensions, 1994, ILLC Prep. Series, ML-94-08,

University of Amsterdam.

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

Report Nr: | DS-1995-02 |

Series Name: | ILLC Dissertation (DS) Series |

Year: | 1995 |

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/1975 |

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