The Seventeen Provers of the World Lecture Notes in Computer Science 3600 Lecture Notes in Artificial Intelligence 1st edition by Freek Wiedijk, Freek Wiedijk ISBN 3540307044  978-3540307044

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ISBN 10: 3540307044
ISBN 13: 978-3540307044
Author: Freek Wiedijk ,Freek Wiedijk

Commemorating the 50th anniversary of the first time a mathematical theorem was proven by a computer system, Freek Wiedijk initiated the present book in 2004 by inviting formalizations of a proof of the irrationality of the square root of two from scientists using various theorem proving systems.

The 17 systems included in this volume are among the most relevant ones for the formalization of mathematics. The systems are showcased by presentation of the formalized proof and a description in the form of answers to a standard questionnaire. The 17 systems presented are HOL, Mizar, PVS, Coq, Otter/Ivy, Isabelle/Isar, Alfa/Agda, ACL2, PhoX, IMPS, Metamath, Theorema, Leog, Nuprl, Omega, B method, and Minlog.

The Seventeen Provers of the World (Lecture Notes in Computer Science 3600 Lecture Notes in Artificial Intelligence) 1st Table of contents:

Preface

• Introduction to Automated Theorem Proving
• Overview of the Different Provers and Their Contributions

Chapter 1: Introduction to Theorem Proving

• Historical Development of Automated Theorem Proving
• Key Concepts: Proofs, Theorems, and Formal Logic
• Importance of Theorem Proving in AI and Computer Science

Chapter 2: Overview of the Seventeen Provers

• Brief Description of Each Prover
• Key Strengths and Weaknesses
• Comparative Analysis of Their Approaches and Techniques

Chapter 3: Provers Based on Resolution

• Principles of Resolution-Based Theorem Proving
• Examples of Resolution Provers
• Applications of Resolution Methods in AI

Chapter 4: Provers Using Tableau and Semantic Methods

• Description of Tableau-Based Methods
• Understanding Semantic Tableaux in Theorem Proving
• Case Studies of Theorem Provers Using Tableau Systems

Chapter 5: Inductive and Declarative Provers

• Inductive Theorem Proving Approaches
• Declarative Systems and Their Applications
• Hybrid Methods Combining Inductive and Declarative Techniques

Chapter 6: Proof Search and Strategies

• Proof Search Algorithms
• Backtracking and Heuristics in Proof Search
• Parallel and Distributed Proof Search

Chapter 7: Applications of Theorem Proving

• Formal Verification and Software Engineering
• Theorem Proving in Artificial Intelligence
• Use of Provers in Cryptography, Security, and Other Fields

Chapter 8: Comparing Provers: Strengths and Limitations

• Performance Benchmarks and Criteria for Evaluation
• Practical Use of Provers in Different Domains
• Case Studies and Real-World Applications

Chapter 9: Advances and Future Directions

• Cutting-Edge Developments in Theorem Proving Technology
• Integration of Machine Learning with Theorem Proving
• The Future of Automated Theorem Proving in AI

Conclusion

• Summary of Key Insights
• The Role of Automated Theorem Proving in AI
• Challenges and Opportunities Ahead for Provers

Appendices

• List of Provers and Relevant Tools
• Additional Resources for Further Study
• Index

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