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## Description

This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

### Readership

Senior college students, and first-year graduate students studying mathematics.

## Table of Contents

Preface

Acknowledgments

1. Introduction

1.1 Artificial Intelligence, Symbolic Logic, and Theorem Proving

1.2 Mathematical Background

References

2. The Propositional Logic

2.1 Introduction

2.2 Interpretations of Formulas in the Propositional Logic

2.3 Validity and Inconsistency in the Propositional Logic

2.4 Normal Forms in the Propositional Logic

2.5 Logical Consequences

2.6 Applications of the Propositional Logic

References

Exercises

3. The First-Order Logic

3.1 Introduction

3.2 Interpretations of Formulas in the First-Order Logic

3.3 Prenex Normal Forms in the First-Order Logic

3.4 Applications of the First-Order Logic

References

Exercises

4. Herbrand's Theorem

4.1 Introduction

4.2 Skolem Standard Forms

4.3 The Herbrand Universe of a Set of Clauses

4.4 Semantic Trees

4.5 Herbrand's Theorem

4.6 Implementation of Herbrand's Theorem

References

Exercises

5. The Resolution Principle

5.1 Introduction

5.2 The Resolution Principle for the Propositional Logic

5.3 Substitution and Unification

5.4 Unification Algorithm

5.5 The Resolution Principle for the First-Order Logic

5.6 Completeness of the Resolution Principle

5.7 Examples Using the Resolution Principle

5.8 Deletion Strategy

References

Exercises

6. Semantic Resolution and Lock Resolution

6.1 Introduction

6.2 An Informal Introduction to Semantic Resolution

6.3 Formal Definitions and Examples of Semantic Resolution

6.

## Details

- No. of pages:
- 331

- Language:
- English

- Copyright:
- © 1973

- Published:
- 28th May 1973

- Imprint:
- Academic Press

- Print ISBN:
- 9780121703509

- Electronic ISBN:
- 9780080917283

## About the authors

### Chin-Liang Chang

#### Affiliations and Expertise

Lockheed Missiles & Space Company, Inc., Menlo Park, CA

### Richard Lee

#### Affiliations and Expertise

National Tsing Hua University, Hsinchu, Taiwan