Automated Theorem Proving: A Logical Basis

Automated Theorem Proving: A Logical Basis

1st Edition - January 1, 1978

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  • Author: D.W. Loveland
  • eBook ISBN: 9781483296777

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Fundamental Studies in Computer Science, Volume 6: Automated Theorem Proving: A Logical Basis aims to organize, augment, and record the major conceptual advances in automated theorem proving. The publication first examines the role of logical systems and basic resolution. Discussions focus on the Davis-Putnam procedure, ground resolution, semantic trees, general resolution procedure, basic concepts of first-order logic, refutation procedures, and preparation of formulas. The text then takes a look at the refinements of resolution, including unit preference and set-of-support, ordered clause deductions, and setting and linear refinements. The monograph tackles subsumption, resolution with equality, and resolution and problem reduction format. Topics include problem reduction format, paramodulation and linear refinements, paramodulation, and subsumption for linear and nonlinear procedures. The publication is a dependable reference for students and researchers interested in automated theorem proving.

Table of Contents

  • Preface



    Chapter 1. The Role of Logical Systems

    1.1. Orientation

    1.2. The Basic Concepts of First-Order Logic

    1.3. The Formal Presentation of Problems

    1.3.1. The Monkey-Banana Problem

    1.3.2. Plane Geometry

    1.3.3. Group Theory

    1.3.4. Elementary Number Theory

    1.4. Refutation Procedures

    1.5. Preparation of Formulas

    1.6. The Herbrand Theorem

    1.7. Summary

    Chapter 2. Basic Resolution

    2.1. Introduction

    2.2. The Davis-Putnam Procedure

    2.3. Ground Resolution

    2.4. Semantic Trees

    2.5. General Resolution: Unification

    2.6. The General Resolution Procedure

    2.7. Summary

    Chapter 3. Refinements of Resolution

    3.1. Introduction

    3.2. Unit Preference and Set-of-Support

    3.3. Ordered Clause Deductions

    3.4. Setting Refinements

    3.5. Linear Refinements

    3.6. Model Elimination

    3.7. Summary

    Chapter 4. Subsumption

    4.1. Subsumption for Nonlinear Procedures

    4.2. Subsumption for Linear Procedures

    4.3. Summary

    Chapter 5. Resolution with Equality

    5.1. Paramodulation

    5.2. Paramodulation and Setting Refinements

    5.3. Paramodulation and Linear Refinements

    5.4. Summary

    Chapter 6. Resolution and Problem Reduction Format

    6.1. The Problem Reduction Format

    6.2. The ME Procedure and Problem Reduction

    6.3. Summary

    Appendix: Resolution-Based Procedures


    Table of Symbols


Product details

  • No. of pages: 418
  • Language: English
  • Copyright: © North Holland 1978
  • Published: January 1, 1978
  • Imprint: North Holland
  • eBook ISBN: 9781483296777

About the Author

D.W. Loveland

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