| Abstract | .... 2 | |
| Contents | .... 3 | |
| 1 | Introduction | .... 3 |
| 1.1 | Motivation and Contents | .... 3 |
| 1.2 | Two Approaches of SLP | .... 5 |
| 2 | Label-based SLP | .... 7 |
| 2.1 | ψ-term Theory | .... 7 |
| 2.2 | Type-based Fimite Automata Theory | .... 9 |
| 2.3 | Computation and Complexity Analyze | .... 10 |
| 2.4 | Substitution and Unification of ψ-terms | .... 11 |
| 3 | Sorted Predicate and SL Program | .... 12 |
| 3.1 | H-term | .... 13 |
| 3.2 | Unification of H-term | .... 14 |
| 3.3 | Horn SLP's Semantics | .... 15 |
| 3.4 | Resolution Method | .... 16 |
| 3.5 | Extended SLP's Semantics | .... 17 |
| 4 | Priority Knowledge and Argument Theory | .... 17 |
| 4.1 | Unit and Standpoint | .... 18 |
| 4.2 | Argument Tree | .... 19 |
| 4.3 | Argument Theory | .... 20 |
| 5 | Comparison with others work | .... 20 |
| 5.1 | Haraguchi's Legal Reasoning System | .... 20 |
| 5.2 | Ait Kati et al's Login and Life | .... 21 |
| 6 | Prakken's Argument Theory | .... 22 |
| 7 | Conclusion | .... 23 |
| Acknowledgments | .... 24 | |
| References | .... 24 | |
| A | Samples of Query | .... 25 |
| B | Semantics of ψ-term | .... 26 |
| C | Algorithms | .... 26 |
| End | .... 28 |
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