| Abstract | .... 2 | |
| 1 | Introduction | .... 3 |
| 2 | Preliminaries | .... 4 |
| 2.1 | Atoms and Molecules | .... 4 |
| 2.2 | General Definite Clause Programs | .... 4 |
| 2.3 | Semantics of General Definite Clause Programs | .... 5 |
| 3 | Transformation of General Definite Clause Programs | .... 8 |
| 3.1 | Transformation Process | .... 6 |
| 3.2 | Basic Transformation Rules | .... 7 |
| 3.3 | Equivalence Preservation Theorem | .... 9 |
| 4 | Preservation of Equivalence | .... 10 |
| 4.1 | Rank and Rank Ordering of Closed Molecule | .... 10 |
| 4.2 | Rank-Consistent Proof | .... 11 |
| 4.3 | Proof of the Equivalence Preservation Theorem | .... 12 |
| 5 | Discussion | .... 18 |
| 6 | Conclusions | .... 19 |
| Acknowledgements | .... 19 | |
| References | .... 19 |
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