The Resolution Calculus

1. Front Matter

   Pages I-VIII

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2. Introduction

   • Alexander Leitsch

   Pages 1-4

3. The Basis of the Resolution Calculus

   • Alexander Leitsch

   Pages 5-87

4. Refinements of Resolution

   • Alexander Leitsch

   Pages 89-147

5. Redundancy and Deletion

   • Alexander Leitsch

   Pages 149-210

6. Resolution as Decision Procedure

   • Alexander Leitch

   Pages 211-252

7. On the Complexity of Resolution

   • Alexander Leitsch

   Pages 253-287

8. Back Matter

   Pages 289-300

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The History of the Book In August 1992 the author had the opportunity to give a course on resolution theorem proving at the Summer School for Logic, Language, and Information in Essex. The challenge of this course (a total of five two-hour lectures) con­ sisted in the selection of the topics to be presented. Clearly the first selection has already been made by calling the course "resolution theorem proving" instead of "automated deduction" . In the latter discipline a remarkable body of knowledge has been created during the last 35 years, which hardly can be presented exhaustively, deeply and uniformly at the same time. In this situ­ ation one has to make a choice between a survey and a detailed presentation with a more limited scope. The author decided for the second alternative, but does not suggest that the other is less valuable. Today resolution is only one among several calculi in computational logic and automated reasoning. How­ ever, this does not imply that resolution is no longer up to date or its potential exhausted. Indeed the loss of the "monopoly" is compensated by new appli­ cations and new points of view. It was the purpose of the course mentioned above to present such new developments of resolution theory. Thus besides the traditional topics of completeness of refinements and redundancy, aspects of termination (resolution decision procedures) and of complexity are treated on an equal basis.

• Decision
• Decision Procederes
• Deduction
• Resolution
• algorithms
• calculus
• complexity

• Intitut für Computersprachen, Technische Universität Wien, Wien, Austria

  Alexander Leitsch

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