Semantics and complexity of recursive aggregates in answer set programming

Artificial Intelligence

Volumn 175, Issue 1, 2011, Pages 278-298

  Faber, Wolfgang ^a   Pfeifer, Gerald ^a   Leone, Nicola ^a  

^a UNIVERSITY OF CALABRIA   (Italy)

Author keywords

Aggregates; Answer set programming; Computational complexity; Nonmonotonic reasoning

Indexed keywords

COMPUTATIONAL COMPLEXITY; LOGIC PROGRAMMING; SEMANTICS;

AGGREGATE-FREE PROGRAMS; ANSWER SET PROGRAMMING; ANSWER SET SEMANTICS; DISJUNCTIVE LOGIC PROGRAMMING; NON-MONOTONIC REASONING; NONMONOTONE AGGREGATES; POLYNOMIAL HIERARCHIES; PROBLEM REPRESENTATION;

AGGREGATES;

EID: 78649721093     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.artint.2010.04.002     Document Type: Article

References (59)

1. W. Faber, N. Leone, and G. Pfeifer Recursive aggregates in disjunctive logic programs: Semantics and complexity J.J. Alferes, J. Leite, Proceedings of the 9th European Conference on Artificial Intelligence (JELIA 2004) Lecture Notes in AI (LNAI) vol. 3229 2004 Springer-Verlag 200 212
2. F. Calimeri, W. Faber, N. Leone, S. Perri, Declarative and computational properties of logic programs with aggregates, in: Nineteenth International Joint Conference on Artificial Intelligence (IJCAI-05), 2005, pp. 406-411.
3. J. McCarthy, Programs with common sense, in: Proceedings of the Teddington Conference on the Mechanization of Thought Processes, Her Majesty's Stationery Office, 1959, pp. 75-91.
4. J. McCarthy, and P.J. Hayes Some philosophical problems from the standpoint of artificial intelligence B. Meltzer, D. Michie, Machine Intelligence vol. 4 1969 Edinburgh University Press 463 502 reprinted in [59]
5. M. Minsky A framework for representing knowledge P.H. Winston, The Psychology of Computer Vision 1975 McGraw-Hill 211 277
6. J. McCarthy Circumscription - A form of non-monotonic reasoning Artificial Intelligence 13 1-2 1980 27 39
7. J. McCarthy Applications of circumscription to formalizing common-sense knowledge Artificial Intelligence 28 1 1986 89 116
8. R. Reiter A logic for default reasoning Artificial Intelligence 13 1-2 1980 81 132
9. D.V. McDermott, and J. Doyle Non-monotonic logic I Artificial Intelligence 13 1-2 1980 41 72
10. D.V. McDermott Non-monotonic logic II: Nonmonotonic modal theories Journal of the ACM 29 1 1982 33 57
11. R.C. Moore Semantical considerations on nonmonotonic logic Artificial Intelligence 25 1 1985 75 94
12. M. Gelfond, and V. Lifschitz Classical negation in logic programs and disjunctive databases New Generation Computing 9 1991 365 385
13. C. Baral Knowledge Representation, Reasoning and Declarative Problem Solving 2003 Cambridge University Press
14. J. Minker On indefinite data bases and the closed world assumption D.W. Loveland, Proceedings of the 6th Conference on Automated Deduction (CADE '82) Lecture Notes in Computer Science vol. 138 1982 Springer New York 292 308
15. T. Eiter, G. Gottlob, and H. Mannila Disjunctive DATALOG ACM Transactions on Database Systems 22 3 1997 364 418
16. P. Simons, I. Niemelä, and T. Soininen Extending and implementing the stable model semantics Artificial Intelligence 138 2002 181 234
17. T. Janhunen, I. Niemelä, D. Seipel, P. Simons, and J.-H. You Unfolding partiality and disjunctions in stable model semantics ACM Transactions on Computational Logic 7 1 2006 1 37
18. N. Leone, G. Pfeifer, W. Faber, T. Eiter, G. Gottlob, S. Perri, and F. Scarcello The DLV system for knowledge representation and reasoning ACM Transactions on Computational Logic 7 3 2006 499 562
19. F. Lin, and Y. Zhao ASSAT: Computing answer sets of a logic program by SAT solvers Artificial Intelligence 157 12 2004 115 137
20. Y. Lierler, and M. Maratea Cmodels-2: SAT-based answer set solver enhanced to non-tight programs V. Lifschitz, I. Niemelä, Proceedings of the 7th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR-7) Lecture Notes in AI (LNAI) vol. 2923 2004 Springer 346 350
21. C. Anger, K. Konczak, and T. Linke NoMoRe: A system for non-monotonic reasoning T. Eiter, W. Faber, M. Truszczyński, Logic Programming and Nonmonotonic Reasoning - Proceedings of the 6th International Conference (LPNMR '01) Vienna, Austria, September 2001 Lecture Notes in AI (LNAI) vol. 2173 2001 Springer-Verlag 406 410
22. C. Anger, M. Gebser, T. Linke, A. Neumann, and T. Schaub The nomore++ approach to answer set solving G. Sutcliffe, A. Voronkov, Logic for Programming, Artificial Intelligence, and Reasoning, 12th International Conference (LPAR 2005) Lecture Notes in Computer Science vol. 3835 2005 Springer-Verlag 95 109
23. M. Gebser, B. Kaufmann, A. Neumann, and T. Schaub Conflict-driven answer set solving Twentieth International Joint Conference on Artificial Intelligence (IJCAI-07) 2007 Morgan Kaufmann Publishers 386 392
24. I.S. Mumick, H. Pirahesh, and R. Ramakrishnan The magic of duplicates and aggregates Proceedings of the 16th International Conference on Very Large Data Bases (VLDB '90) 1990 Morgan Kaufmann 264 277
25. D.B. Kemp, and P.J. Stuckey Semantics of logic programs with aggregates V.A. Saraswat, K. Ueda, Proceedings of the International Symposium on Logic Programming (ISLP '91) 1991 MIT Press 387 401
26. K.A. Ross, and Y. Sagiv Monotonic aggregation in deductive databases Journal of Computer and System Sciences 54 1 1997 79 97
27. M. Gelfond Representing knowledge in A-Prolog A.C. Kakas, F. Sadri, Computational Logic. Logic Programming and Beyond Lecture Notes in Computer Science vol. 2408 2002 Springer 413 451
28. T. Dell'Armi, W. Faber, G. Ielpa, N. Leone, and G. Pfeifer Aggregate functions in DLV in: M. de Vos, A. Provetti (Eds.), Proceedings ASP03 - Answer Set Programming: Advances in Theory and Implementation, Messina, Italy, 2003, pp. 274-288, online at http://CEUR-WS.org/Vol-78/
29. N. Pelov, M. Denecker, and M. Bruynooghe Partial stable models for logic programs with aggregates Proceedings of the 7th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR-7) Lecture Notes in AI (LNAI) vol. 2923 2004 Springer 207 219
30. N. Pelov, M. Truszczyński, Semantics of disjunctive programs with monotone aggregates - An operator-based approach, in: Proceedings of the 10th International Workshop on Non-Monotonic Reasoning (NMR 2004), Whistler, BC, Canada, 2004, pp. 327-334.
31. V.W. Marek, J.B. Remmel, On logic programs with cardinality constraints, in: S. Benferhat, E. Giunchiglia (Eds.), Proceedings of the 9th International Workshop on Non-Monotonic Reasoning (NMR 2002), Toulouse, France, 2002, pp. 219-228.
32. V.W. Marek, and J.B. Remmel Set constraints in logic programming V. Lifschitz, I. Niemelä, Proceedings of the 7th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR-7) Lecture Notes in AI (LNAI) vol. 2923 2004 Springer 167 179
33. V.W. Marek, I. Niemelä, and M. Truszczyński Logic programming with monotone cardinality atom V. Lifschitz, I. Niemelä, Proceedings of the 7th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR-7) Lecture Notes in AI (LNAI) vol. 2923 2004 Springer 154 166
34. N. Pelov, M. Denecker, and M. Bruynooghe Well-founded and stable semantics of logic programs with aggregates Theory and Practice of Logic Programming 7 3 2007 301 353
35. T.C. Son, and E. Pontelli A constructive semantic characterization of aggregates in ASP Theory and Practice of Logic Programming 7 2007 355 375
36. T.C. Son, E. Pontelli, I. Elkabani, On logic programming with aggregates, Tech. Rep. NMSU-CS-2005-006, New Mexico State University, 2005.
37. P. Ferraris Answer sets for propositional theories C. Baral, G. Greco, N. Leone, G. Terracina, Logic Programming and Nonmonotonic Reasoning - 8th International Conference (LPNMR '05) Diamante, Italy, September 2005 Lecture Notes in Computer Science vol. 3662 2005 Springer-Verlag 119 131
38. T. Dell'Armi, W. Faber, G. Ielpa, N. Leone, and G. Pfeifer Aggregate functions in disjunctive logic programming: Semantics, complexity, and implementation in DLV Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI) 2003 2003 Morgan Kaufmann Publishers Acapulco, Mexico 847 852
39. F. Lin, and Y. Zhao ASSAT: Computing answer sets of a logic program by SAT solvers Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI 2002) 2002 AAAI Press/MIT Press Edmonton, Alberta, Canada
40. J.D. Ullman Principles of Database and Knowledge Base Systems 1989 Computer Science Press
41. K.R. Apt, H.A. Blair, and A. Walker Towards a theory of declarative knowledge J. Minker, Foundations of Deductive Databases and Logic Programming 1988 Morgan Kaufmann Publishers, Inc. Washington, DC 89 148
42. T.C. Przymusinski On the declarative semantics of deductive databases and logic programs J. Minker, Foundations of Deductive Databases and Logic Programming 1988 Morgan Kaufmann Publishers, Inc. 193 216
43. I. Niemelä, P. Simons, and T. Soininen Stable model semantics of weight constraint rules M. Gelfond, N. Leone, G. Pfeifer, Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR '99) Lecture Notes in AI (LNAI) vol. 1730 1999 Springer-Verlag El Paso, Texas, USA 107 116
44. W. Faber, Decomposition of nonmonotone aggregates in logic programming, in: M. Fink, H. Tompits, S. Woltran (Eds.), Proceedings of the 20th Workshop on Logic Programming (WLP 2006), Vienna, Austria, 2006, pp. 164-171.
45. E. Dantsin, T. Eiter, G. Gottlob, and A. Voronkov Complexity and expressive power of logic programming ACM Computing Surveys 33 3 2001 374 425
46. G. Gottlob, N. Leone, and H. Veith Succinctness as a source of expression complexity Annals of Pure and Applied Logic 97 13 1999 231 260
47. L.J. Stockmeyer, and A.R. Meyer Word problems requiring exponential time: Preliminary report Conference Record of 5th Annual ACM Symposium on Theory of Computing (STOC '73) 1973 ACM Press 1 9
48. V.W. Marek, and M. Truszczyński Autoepistemic logic Journal of the ACM 38 3 1991 588 619
49. T. Eiter, and G. Gottlob On the computational cost of disjunctive logic programming: Propositional case Annals of Mathematics and Artificial Intelligence 15 3/4 1995 289 323
50. N. Pelov, Semantics of logic programs with aggregates, Ph.D. thesis, Katholieke Universiteit Leuven, Leuven, Belgium, Apr. 2004.
51. T. Eiter, G. Gottlob, and H. Veith Modular logic programming and generalized quantifiers J. Dix, U. Furbach, A. Nerode, Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR '97) Lecture Notes in Computer Science vol. 1265 1997 Springer 290 309
52. P. Ferraris, and V. Lifschitz Weight constraints as nested expressions Theory and Practice of Logic Programming 5 1-2 2005 45 74
53. V. Lifschitz, L.R. Tang, and H. Turner Nested expressions in logic programs Annals of Mathematics and Artificial Intelligence 25 34 1999 369 389
54. J. Lee, V. Lifschitz, and R. Palla A reductive semantics for counting and choice in answer set programming D. Fox, C.P. Gomes, Proceedings of the 23rd National Conference on Artificial Intelligence (AAAI '08) 2008 AAAI Press 472 479
55. P. Ferraris, J. Lee, V. Lifschitz, A new perspective on stable models, in: Twentieth International Joint Conference on Artificial Intelligence (IJCAI-07), 2007, pp. 372-379.
56. T. Eiter, G. Ianni, R. Schindlauer, H. Tompits, A uniform integration of higher-order reasoning and external evaluations in answer set programming, in: International Joint Conference on Artificial Intelligence (IJCAI 2005), Edinburgh, UK, 2005, pp. 90-96.
57. T. Eiter, G. Ianni, H. Tompits, R. Schindlauer, Effective integration of declarative rules with external evaluations for semantic web reasoning, in: Proceedings of the 3rd European Semantic Web Conference (ESWC 2006), 2006, pp. 273-287.
58. T.C. Son, E. Pontelli, and P.H. Tu Answer sets for logic programs with arbitrary abstract constraint atoms Journal of Artificial Intelligence Research 29 2007 353 389
59. J. McCarthy Formalization of Common Sense papers by John McCarthy edited by V. Lifschitz 1990 Ablex