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Item Details
| Title:
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METHODS OF CUT-ELIMINATION
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| By: |
Matthias Baaz, Alexander Leitsch |
| Format: |
Hardback |
| List price:
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£109.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
9400703198 |
| ISBN 13: |
9789400703193 |
| Publisher: |
SPRINGER |
| Pub. date: |
14 January, 2011 |
| Edition: |
2011 |
| Series: |
Trends in Logic 34 |
| Pages: |
290 |
| Description: |
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. |
| Synopsis: |
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. |
| Illustrations: |
VI, 290 p. |
| Publication: |
Netherlands |
| Imprint: |
Springer |
| Returns: |
Returnable |
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