Téléchargez le livre : Methods of Cut-Elimination

Methods of Cut-Elimination

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Éditeur :

Springer


Collection :

Trends in Logic

Paru le : 2011-01-07

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Description

This is the first book on cut-elimination in first-order predicate logic from an algorithmic point of view. Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs). The first part investigates traditional reductive methods from the point of view of proof rewriting. Within this general framework, generalizations of Gentzen's and Sch\”utte-Tait's cut-elimination methods are defined and shown terminating with ACNFs of the original proof. Moreover, a complexity theoretic comparison of Gentzen's and Tait's methods is given.
The core of the book centers around the cut-elimination method CERES (cut elimination by resolution) developed by the authors. CERES is based on the resolution calculus and radically differs from the reductive cut-elimination methods. The book shows that CERES asymptotically outperforms all reductive methods based on Gentzen's cut-reduction rules. It obtains this result by heavy use of subsumption theorems in clause logic. Moreover, several applications of CERES are given (to interpolation, complexity analysis of cut-elimination, generalization of proofs, and to the analysis of real mathematical proofs). Lastly, the book demonstrates that CERES can be extended to nonclassical logics, in particular to finitely-valued logics and to G\"odel logic.
Pages
290 pages
Collection
Trends in Logic
Parution
2011-01-07
Marque
Springer
EAN papier
9789400703193
EAN EPUB
9789400703209
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
29
Taille du fichier
6748 Ko
Prix
94,94 €

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