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Représentation et interaction des preuves en superdéduction modulo

Clément Houtmann 1
1 PAREO - Formal islands: foundations and applications
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this thesis we propose and study several deduction systems that mix deduction and computation. Deduction modulo proposes to translate a computational power through a rewriting system. We present the dual concept called superdeduction. It translates a deductive power into custom inference rules that enrich the deduction system. These computational and deductive powers modify the representation of proofs as well as their interaction through cut-elimination processes. Strong normalisation or cut-admissibility may be lost and therefore appear as intrinsic properties of theories represented as rewriting systems. We prove that certain criteria imply these properties by defining a proof-term language for superdeduction and by studying the permutability of inferences in classical sequent calculus. Our attention is focused on classical sequent calculi and on the representation of proofs in such systems. Other related paradigms are considered, namely proof-nets and focusing. We compare this latter approach with superdeduction. We consequently reforge the superdeduction paradigm on top of a multifocusing system for classical logic. We demonstrate the benefits of this approach by proving the completeness of the obtained deduction systems.
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Clément Houtmann. Représentation et interaction des preuves en superdéduction modulo. Génie logiciel [cs.SE]. Université Henri Poincaré - Nancy I, 2010. Français. ⟨NNT : 2010NAN10026⟩. ⟨tel-00553219⟩

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