Ebook: Automated Theorem Proving: Theory and Practice
Author: Monty Newborn (auth.)
- Tags: Mathematical Logic and Foundations, Mathematical Logic and Formal Languages, Artificial Intelligence (incl. Robotics)
- Year: 2001
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of inference. This also includes a description of a third program included with this package, called COMPILE. As described in Chapter 3, COMPILE transforms predicate calculus expressions into clause form as required by HERBY and THEO. Chapter 5 presents the theoretical foundations of seman tic tree theorem proving as performed by HERBY. Chapter 6 presents the theoretical foundations of resolution-refutation theorem proving as per formed by THEO. Chapters 7 and 8 describe HERBY and how to use it.
Content:
Front Matter....Pages i-xiv
A Brief Introduction to Compile, Herby, and Theo....Pages 1-6
Predicate Calculus, Well-Formed Formulas, and Theorems....Pages 7-20
Compile: Transforming Well-Formed Formulas to Clauses....Pages 21-28
Inference Procedures....Pages 29-42
Proving Theorems by Constructing Closed Semantic Trees....Pages 43-52
Resolution-Refutation Proofs....Pages 53-84
Herby: A Semantic—Tree Theorem Prover....Pages 85-96
Using Herby....Pages 97-112
Theo:A Resolution—Refutation Theorem Prover....Pages 113-138
Using Theo....Pages 139-159
A Look at the Source Code of Herby....Pages 161-172
A Look at the Source Code of Theo....Pages 173-180
The Cade Atp System Competitions and Other Theorem Provers....Pages 181-206
Back Matter....Pages 207-231
Content:
Front Matter....Pages i-xiv
A Brief Introduction to Compile, Herby, and Theo....Pages 1-6
Predicate Calculus, Well-Formed Formulas, and Theorems....Pages 7-20
Compile: Transforming Well-Formed Formulas to Clauses....Pages 21-28
Inference Procedures....Pages 29-42
Proving Theorems by Constructing Closed Semantic Trees....Pages 43-52
Resolution-Refutation Proofs....Pages 53-84
Herby: A Semantic—Tree Theorem Prover....Pages 85-96
Using Herby....Pages 97-112
Theo:A Resolution—Refutation Theorem Prover....Pages 113-138
Using Theo....Pages 139-159
A Look at the Source Code of Herby....Pages 161-172
A Look at the Source Code of Theo....Pages 173-180
The Cade Atp System Competitions and Other Theorem Provers....Pages 181-206
Back Matter....Pages 207-231
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