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A General View of Normalisation through Atomic Flows

Tom Gundersen 1, 2
2 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : 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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Contributor : Tom Gundersen <>
Submitted on : Wednesday, August 11, 2010 - 4:46:00 AM
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  • HAL Id : tel-00441540, version 3



Tom Gundersen. A General View of Normalisation through Atomic Flows. Mathematics [math]. The University of Bath, 2009. English. ⟨tel-00441540v3⟩



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