First-Order Logic and Automated Theorem Proving

1. Front Matter

   Pages i-xvii

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2. Background

   • Melvin Fitting

   Pages 1-8

3. Propositional Logic

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   Pages 9-39

4. Semantic Tableaux and Resolution

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   Pages 41-76

5. Other Propositional Proof Procedures

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   Pages 77-107

6. First-Order Logic

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   Pages 109-136

7. First-Order Proof Procedures

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   Pages 137-150

8. Implementing Tableaux and Resolution

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   Pages 151-201

9. Further First-Order Features

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   Pages 203-269

10. Equality

    • Melvin Fitting

    Pages 271-313

11. Back Matter

    Pages 315-326

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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.

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

• Department of Mathematics and Computer Science Lehman College, The City of New York University, Bronx, USA

  Melvin Fitting

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