Methods of Cut-Elimination: 34 (Trends in Logic, 34) - Image 1

£76.41

Springer Methods of Cut-Elimination: 34 (Trends in Logic, 34)

Name: Methods of Cut-Elimination: 34 (Trends in Logic, 34)
Brand: Springer
Price: 76.41 GBP
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Programming

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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.

Product Specifications

Brand: Springer
Format: paperback
ASIN: 9400734972
Category: Books > Subjects > Computing & Internet > Programming
Domain: Amazon UK
Publication Date: 25 February 2013
Listed Since: 08 February 2013

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Springer Methods of Cut-Elimination: 34 (Trends in Logic, 34)

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