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Methods of Cut-Elimination - Alexander Leitsch#Matthias Baaz
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Alexander Leitsch#Matthias Baaz:
Methods of Cut-Elimination - nieuw boek

ISBN: 9789400703193

ID: 1943133451

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. This book offers a thorough, rigorous analysis of reductive cut-elimination methods and an in-depth presentation of the recent method CERES developed by the authors. It includes several applications of CERES and an extension of CERES to non-classical logics. Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer

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Methods of Cut-Elimination - Matthias Baaz; Alexander Leitsch
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Matthias Baaz; Alexander Leitsch:
Methods of Cut-Elimination - gebonden uitgave, pocketboek

ISBN: 9789400703193

ID: 9789400703193

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. Books > Mathematics Hard cover, Springer Shop

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Methods of Cut-Elimination
(*)
Methods of Cut-Elimination - nieuw boek

ISBN: 9789400703193

ID: MOLEGLSGJ4B

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. Bücher / Naturwissenschaften, Medizin, Informatik & Technik / Mathematik / Grundlagen

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Methods of Cut-Elimination - Alexander Leitsch
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Alexander Leitsch:
Methods of Cut-Elimination - nieuw boek

2001, ISBN: 9789400703193

[ED: Buch], [PU: Springer-Verlag GmbH], Neuware - 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., DE, Neuware, gewerbliches Angebot, 243x167x27 mm, 287, [GW: 578g], offene Rechnung (Vorkasse vorbehalten), PayPal, Banküberweisung

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Methods of Cut-Elimination - Baaz, Matthias; Leitsch, Alexander
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Baaz, Matthias; Leitsch, Alexander:
Methods of Cut-Elimination - nieuw boek

ISBN: 9789400703193

ID: 666739

This book offers a thorough, rigorous analysis of reductive cut-elimination methods and an in-depth presentation of the recent method CERES developed by the authors. It includes several applications of CERES and an extension of CERES to non-classical logics. Computers Computers eBook, Springer Netherlands

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Bijzonderheden over het boek
Methods of Cut-Elimination

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.

Gedetalleerde informatie over het boek. - Methods of Cut-Elimination


EAN (ISBN-13): 9789400703193
ISBN (ISBN-10): 9400703198
Gebonden uitgave
Verschijningsjaar: 2011
Uitgever: Springer
287 Bladzijden
Gewicht: 0,578 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 25.09.2008 21:54:20
Boek voor het laatst gevonden op 09.04.2019 19:34:34
ISBN/EAN: 9789400703193

ISBN - alternatieve schrijfwijzen:
94-007-0319-8, 978-94-007-0319-3


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