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On elementary loops of logic programs
| Content Provider | Scilit |
|---|---|
| Author | Gebser, Martin Lee, Joohyung Lierler, Yuliya |
| Copyright Year | 2011 |
| Description | Using the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), 53–65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53–87). Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body. |
| Related Links | http://arxiv.org/pdf/1012.5847 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/63EFEC4A838BA207CDA3D29B53AFE21C/S1471068411000019a.pdf/div-class-title-on-elementary-loops-of-logic-programs-div.pdf |
| Ending Page | 988 |
| Page Count | 36 |
| Starting Page | 953 |
| ISSN | 14710684 |
| e-ISSN | 14753081 |
| DOI | 10.1017/s1471068411000019 |
| Journal | Theory and Practice of Logic Programming |
| Issue Number | 6 |
| Volume Number | 11 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2011-11-01 |
| Access Restriction | Open |
| Subject Keyword | Theory and Practice of Logic Programming Stable Model Semantics Loop Formulas Unfounded Sets |
| Content Type | Text |
| Resource Type | Article |
| Subject | Artificial Intelligence Theoretical Computer Science Computational Theory and Mathematics Hardware and Architecture Software |
