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| Detailed view | PhD thesis |
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| The University of Bath (10/11/2009), Alessio Guglielmi (Dir.) |
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| Available versions: | v1 (2009-12-16) | v2 (2009-12-17) |
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| A General View of Normalisation through Atomic Flows |
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| Tom Gundersen1 |
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| 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 deep-inference 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. |
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| 1: | LIX - Laboratoire d'informatique de l'école polytechnique |
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| 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 deep-inference 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 |
| tel-00441540, version 2 | |
| http://tel.archives-ouvertes.fr/tel-00441540/en/ | |
| oai:tel.archives-ouvertes.fr:tel-00441540_v2 | |
| From: Tom Gundersen | |
| Submitted on: Thursday, 17 December 2009 02:27:50 | |
| Updated on: Thursday, 17 December 2009 08:27:46 | |
