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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.

First-order logic. --- Proof theory. --- Logic, Symbolic and mathematical --- Logic, Modern --- Logic, Symbolic and mathematical. --- Computer science. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Informatics --- Science --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematical logic.

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This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.

Automatic theorem proving --- Logic, Symbolic and mathematical --- Congresses. --- Computer Science --- Engineering & Applied Sciences --- Congresses --- Mathematics. --- Programming languages (Electronic computers). --- Algorithms. --- Mathematical logic. --- Artificial intelligence. --- Mathematical Logic and Foundations. --- Programming Languages, Compilers, Interpreters. --- Artificial Intelligence (incl. Robotics). --- Mathematical Logic and Formal Languages. --- Algorithm Analysis and Problem Complexity. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algorism --- Algebra --- Arithmetic --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- Math --- Science --- Foundations --- Logic [Symbolic and mathematical ] --- Logic, Symbolic and mathematical. --- Computer science. --- Computer software. --- Artificial Intelligence. --- Software, Computer --- Computer systems --- Informatics --- Automatic theorem proving - Congresses. --- Logic, Symbolic and mathematical - Congresses

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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.

Mathematical logic --- wiskunde

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Automatic theorem proving --- Computer logic --- Computer Science --- Engineering & Applied Sciences --- Artificial intelligence. --- Logic design. --- Design, Logic --- Design of logic systems --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Computer science. --- Software engineering. --- Computer logic. --- Mathematical logic. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Mathematical Logic and Formal Languages. --- Logics and Meanings of Programs. --- Software Engineering. --- Mathematical Logic and Foundations. --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer science logic --- Logic, Symbolic and mathematical --- Computer software engineering --- Engineering --- Informatics --- Science --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Logic, Symbolic and mathematical. --- Artificial Intelligence. --- Congresses --- Automatic theorem proving - Congresses --- Computer logic - Congresses