Graph-Based Proof Procedures for Horn Clauses

1. Front Matter

   Pages i-viii

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2. Introduction

   • Stan Raatz

   Pages 1-6

3. Preliminaries

   • Stan Raatz

   Pages 7-20

4. A Semantics for the Hornlog System

   • Stan Raatz

   Pages 21-35

5. The Hornlog Proof Procedure

   • Stan Raatz

   Pages 36-53

6. Soundness and Completeness Results I

   • Stan Raatz

   Pages 54-76

7. An Equational Extension

   • Stan Raatz

   Pages 77-87

8. The He ^† Refutation Method

   • Stan Raatz

   Pages 88-105

9. Soundness and Completeness Results II

   • Stan Raatz

   Pages 106-126

10. Appendix: Implementation Issues

    • Stan Raatz

    Pages 127-141

11. Bibliography

    • Stan Raatz

    Pages 142-147

12. Back Matter

    Pages 149-150

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The origins of this monograph lie in my Ph.D. dissertation of 1987 at the University of Pennsylvania, which was concerned with proof procedures for the Horn clause subset of logic. The rise of logic programming has made this an important area of study. All Prologs are based on a variant of resolution, and inherit various properties related to this proof method. This monograph studies the paradigm of logic programming in the context of graph-based proof procedures which are unrelated to resolution. The monograph is not a general introduction to logic programming, although it is self-contained with respect to the mathematics used. It should appeal to the computer scientist or mathematician interested in the general area we now call computational logic. A large part of the monograph is devoted to detailed proofs that the methods we present are sound and complete, which in the context of the logic programming, means that the operational and denotational semantics agree.

• logic
• Resolution
• semantics

• Department of Computer Science, Rutgers University, New Brunswick, USA

  Stan Raatz

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