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Methods of Cut-Elimination
Trends in Logic 34
ISBN/EAN: 9789400734975
Umbreit-Nr.: 4428215
Sprache:
Englisch
Umfang: vi, 290 S., 360 s/w Illustr.
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 25.02.2013
Auflage: 1/2013
- Zusatztext
- 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.
- Kurztext
- This book on methods of cut-elimination contains a thorough and rigorous analysis of reductive cut-elimination methods and an in-depth presentation of the recent method CERES developed by the authors. It includes a detailed complexity analysis and comparison of CERES and of reductive methods. It presents several applications of CERES-to interpolation, fast cut-elimination, generalization of proofs and to the analysis of mathematical proofs. Finally, it provides an extension of CERES to non-classical logics, in particular to finitely-valued logics and to Gödel logic.
- Autorenportrait
- Inhaltsangabe1 Preface.- 2 Introduction.- 3 Preliminaries.- 4 Complexity of Cut-Elimination.- 5 Reduction and Elimination.- 6 Cut-Elimination by Resolution.- 7 Extensions of CERES.- 8 Applications of CERES.- 9 CERES in Nonclassical Logics.- 10 Related Research.