A General View of Normalisation through Atomic Flows

Tom Gundersen (1, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 CALLIGRAMME - Linear logic, proof networks and categorial grammars

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.

Keywords: normalisation; deep inference; atomic flows; propositional logic; cut elimination

Domains: Mathematics [math]; Other [cs.OH]

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