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Combines techniques and results from proof theory and automated deduction
Provides a completely new view on proof theoretic methods and their applications, which makes the book interesting for researchers and graduate students in proof theory and computational logic
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.
1 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.