Symbolic Logic and Mechanical Theorem Proving

1st Edition

Authors: Chin-Liang Chang Richard Lee
Hardcover ISBN: 9780121703509
eBook ISBN: 9780080917283
Imprint: Academic Press
Published Date: 28th May 1973
Page Count: 331
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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:
© Academic Press 1973
Published:
Imprint:
Academic Press
eBook ISBN:
9780080917283
Hardcover ISBN:
9780121703509

About the Author

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

Reviews

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.