# First-Order Logic and Automated Theorem Proving

• Melvin Fitting
Book

Part of the Graduate Texts in Computer Science book series (TCS)

1. Front Matter
Pages i-xvii
2. Melvin Fitting
Pages 1-8
3. Melvin Fitting
Pages 9-39
4. Melvin Fitting
Pages 41-76
5. Melvin Fitting
Pages 77-107
6. Melvin Fitting
Pages 109-136
7. Melvin Fitting
Pages 137-150
8. Melvin Fitting
Pages 151-201
9. Melvin Fitting
Pages 203-269
10. Melvin Fitting
Pages 271-313
11. Back Matter
Pages 315-326

### Introduction

There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scien­ tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer science formal logic turns up in a number of areas, from pro­ gram verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theo­ rem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but, not incompleteness issues. The first item to be addressed is, What are we talking about and why are we interested in it? We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self­ evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

### Keywords

Cut-elimination theorem Resolution Variable automated theorem proving calculus complexity computer formal logic logic proof semantics sequent calculus theorem proving

#### Authors and affiliations

• Melvin Fitting
• 1
1. 1.Department of Mathematics and Computer Science Lehman CollegeThe City of New York UniversityBronxUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-2360-3
• Copyright Information Springer-Verlag New York 1996
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-7515-2
• Online ISBN 978-1-4612-2360-3
• Series Print ISSN 1868-0941
• Series Online ISSN 1868-095X