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Methods of Cut-Elimination (Hardcover, 2011) Loot Price: R2,957
Discovery Miles 29 570
Methods of Cut-Elimination (Hardcover, 2011): Matthias Baaz, Alexander Leitsch

Methods of Cut-Elimination (Hardcover, 2011)

Matthias Baaz, Alexander Leitsch

Series: Trends in Logic, 34

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Loot Price R2,957 Discovery Miles 29 570 | Repayment Terms: R277 pm x 12*

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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.

General

Imprint: Springer
Country of origin: Netherlands
Series: Trends in Logic, 34
Release date: 2011
First published: 2011
Authors: Matthias Baaz • Alexander Leitsch
Dimensions: 235 x 155 x 24mm (L x W x T)
Format: Hardcover
Pages: 290
Edition: 2011
ISBN-13: 978-9400703193
Categories: Books > Computing & IT > General theory of computing > Mathematical theory of computation
Books > Science & Mathematics > Mathematics > Mathematical foundations > General
LSN: 9400703198
Barcode: 9789400703193

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