Detailed view  PhD thesis 
The University of Bath (20091110), Alessio Guglielmi (Dir.) 
Available versions:  v1 (20091216)  v2 (20091217)  v3 (20100812) 
Attached file list to this document:  

A General View of Normalisation through Atomic Flows 
Tom Gundersen^{1, 2} 
Atomic ﬂows are a geometric invariant of classical propositional proofs in deep inference. In this thesis we use atomic ﬂows to describe new normal forms of proofs, of which the traditional normal forms are special cases, we also give several normalisation procedures for obtaining the normal forms. We deﬁne, and use to present our results, a new deepinference formalism called the functorial calculus, which is more ﬂexible than the traditional calculus of structures. To our surprise we are able to 1) normalise proofs without looking at their logical connectives or logical rules; and 2) normalise proofs in less than exponential time. 
1:  LIX  Laboratoire d'informatique de l'école polytechnique 
2:  INRIA Lorraine  LORIA  CALLIGRAMME 
normalisation – deep inference – atomic flows – propositional logic – cut elimination 
A General View of Normalisation through Atomic Flows 
Atomic ﬂows are a geometric invariant of classical propositional proofs in deep inference. In this thesis we use atomic ﬂows to describe new normal forms of proofs, of which the traditional normal forms are special cases, we also give several normalisation procedures for obtaining the normal forms. We deﬁne, and use to present our results, a new deepinference formalism called the functorial calculus, which is more ﬂexible than the traditional calculus of structures. To our surprise we are able to 1) normalise proofs without looking at their logical connectives or logical rules; and 2) normalise proofs in less than exponential time. 
normalisation – deep inference – atomic flows – propositional logic – cut elimination 
tel00441540, version 3  
http://tel.archivesouvertes.fr/tel00441540  
oai:tel.archivesouvertes.fr:tel00441540  
From: Tom Gundersen  
Submitted on: Wednesday, 11 August 2010 04:46:00  
Updated on: Thursday, 7 July 2011 10:30:21 