Optimal Models of Disjunctive Logic Programs: Semantics, Complexity, and Computation

IEEE Transactions on Knowledge and Data Engineering

Volumn 16, Issue 4, 2004, Pages 487-503

  Leone, Nicola ^a   Scarcello, Francesco ^a   Subrahmanian, V S ^b  

^a UNIVERSITY OF CALABRIA   (Italy)

^b Institute of Advanced Computer Science   (United States)

Author keywords

Computational complexity; Disjunctive logic programming; Knowledge representation; Nonmonotonic reasoning; Optimization problems

Indexed keywords

DISJUNCTIVE LOGIC PROGRAMMING; HERBRAND OBJECTIVE FUNCTION; NONMONOTONIC REASONING;

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTER SOFTWARE; DATABASE SYSTEMS; KNOWLEDGE REPRESENTATION; LOGIC PROGRAMMING; MATHEMATICAL MODELS; OPTIMIZATION; SET THEORY;

SEMANTICS;

EID: 2142760103     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2004.1269672     Document Type: Article

References (36)

1. P. Barth and A. Bockmayr, "Modelling Discrete Optimization Problems in Constraint Logic Programming," Annals of Operations Research, vol. 81, pp. 467-496, 1998.
2. M. Cadoli, "On the Complexity of Model Finding for Nonmonotonic. Propositional Logics," Proc. Fourth Italian Conf. Theoretical Computer Science, M. Venturini Zilli, A. Marchetti Spaccamela, and P. Mentrasti, eds. Singapore: World Scientific, pp. 125-139, 1992.
3. J. Cohen, "Constraint Logic Programming," Comm. ACM., vol. 33, no. 7, 1990.
4. P. Dasgupta, P.P. Chakrabarti, A. Dey, S. Chose, and W. Bibel, "Solving Constraint Optimization Problems from CLP-Style Specifications Using Heuristic Search Techniques," IEEE Trans. Knowledge and Data Eng., vol. 14, no. 2, pp. 353-368, 2002.
5. M. Dincbas, H. Simonis, and P. Van Hentenryck, "Solving Large Combinatorial Optimization Problems in Logic Programming," J. Logic Programming, vol. 8, nos. 1-2, pp. 75-93, 1990.
6. J. Dix and F. Stolzenburg, "Computation of Non-Ground Disjunctive Well-Founded Semantics with Constraint Logic Programming," Proc. Workshop Nonmonotonic Extensions of Logic Programming, pp. 202-224, 1996.
7. T. Eiter and G. Gottlob, "On the Computational Cost of Disjunctive Logic Programming: Propositional Case," Annals of Math. and Artificial Intelligence, vol. 15, nos. 3-4, pp. 289-323, 1995.
8. T. Eiter, G. Gottlob, and H. Mannila, "Disjunctive Datalog," ACM Trans. Database Systems, vol. 22, no. 3, pp. 364-418, 1997.
9. M.C. Fitting, "Logic Programming on a Topological Bilattice," Fundamenta Informatica, vol. 11, pp. 209-218, 1988.
10. M. Gelfond and V. Lifschitz, "The Stable Model Semantics for Logic Programming," Logic Programming: Proc. Fifth Int'l Conf. Symp., pp. 1070-1080, 1988.
11. M. Gelfond and V. Lifschitz, "Classical Negation in Logic Programs and Disjunctive Databases," New Generation Computing, vol. 9, pp. 365-385, 1991.
12. J. Jaffar and J.-L. Lassez, "Constraint Logic Programming," Proc. 14th ACM Symp. Principles of Programming Languages, 1987.
13. D.S. Johnson, "A Catalog of Complexity Classes," Handbook of Theoretical Computer Science, J. van Leeuwen, ed., vol. A, chapter 2, B.V. (North-Holland): Elsevier Science, pp. 67-161, 1990.
14. (NP[O(log n)1) and Sparse Turing-Complete Sets for NP," J. Computer and System Sciences, vol. 39, no. 3, pp. 282-298, 1989.
15. M. Kifer and V.S. Subrahmanian, "Theory of Generalized Annotated Logic Programming and Its Applications," J. Logic Programming, vol. 12, no. 4, pp. 335-368, 1992.
16. C. Koch and N. Leone, "Stable Model Checking Made Easy," Proc. 16th Int'l Joint Conf. Artificial Intelligence, Thomas Dean, ed., Morgan Kaufmann, pp. 70-75, Aug. 1999.
17. V.S. Lakshmanan and F. Sadri, "Modeling Uncertainty in Deductive Databases," Proc. Int'l Conf. Database Expert Systems and Applications, pp. 724-733, Sept. 1994.
18. V.S. Lakshmanan and F. Sadri, "Probabilistic Deductive Databases," Proc. Int'l Logic Programming Symp., Nov. 1994.
19. V.S. Lakshmanan and N. Shiri, "A Parametric Approach with Deductive Databases with Uncertainty," IEEE Trans. Knowledge and Data Eng., 1997.
20. N. Leone, F. Scarcello, and V.S. Subrahmanian, "Optimal Models of Disjunctive Logic Programs: Semantics, Complexity, and Computation," Univ. of Maryland Technical Report CS-TR-4298, www.cs.umd.e.du/Library/TRs/CS-TR-4298. ps.Z, 2001.
21. N. Leone, P. Rullo, and F. Scarcello, "Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics and Computation," Information and Computation, vol. 135, no. 2, pp. 69-112, June 1997.
22. J.W. Lloyd, Foundations of Logic Programming. Springer-Verlag, 1987.
23. V.W. Marek and M. Truszczynski, "Logic Programming with Cost," unpublished manuscript, 1999.
24. K. Marriot and P.]. Stuckey, Programming with Constraints: An Introduction. MIT Press, 1998.
25. J. Minker, "On Indefinite Data Bases and the Closed World Assumption," Proc. Sixth Conf. Automated Deduction, D.W. Loveland, ed., pp. 292-308, 1982.
26. R. Ng and V.S. Subrahmanian, "Probabilistic Logic Programming, Information and Computation," Information and Computation, vol. 101, no. 2, pp. 150-201, Dec. 1992.
27. T. Niemela, P. Simons, and T. Soininen, "Extending and Implementing the Stable Model Semantics," Artificial Intelligence, vol. 138, nos. 1-2, pp. 181-234, 2002.
28. C.H. Papadimitriou, Computational Complexity. Addison-Wesley, 1994.
29. F. Rossi, "Constraint (Logic) Programming: A Survey on Research and Applications," New Trends in Constraints, 1999.
30. D. Saccà and C. Zaniolo, "Stable Models and Non-Determinism in Logic Programs with Negation," Proc. Ninth Symp. Principles of Database Systems, pp. 205-217, 1990.
31. T. Sandholm, "Algorithm for Optimal Winner Determination in Combinatorial Auctions," Artificial Intelligence, vol. 135, nos. 1-2, 2002.
32. E. Shapiro, "Logic Programs with Uncertainties: A Tool for Implementing Expert Systems," Proc. Int'l Joint Conf. Artificial Intelligence, pp. 529-532, 1983.
33. M. Shiri, "On a Generalized Theory of Deductive Databases," PhD dissertation, Concordia Univ., Montreal, Canada, Aug. 1997.
34. M.Y. Vardi, "The Complexity of Relational Query Languages (extended abstract)," Proc. 14th ACM. Symp. Theory of Computing, pp. 137-146, 1982.
35. P. Van Hentenryck, "A Logic Language for Combinatorial Optimization," Annals of Operations Research, vol. 21, pp. 247-274, 1990.
36. M.H. van Emden, "Quantitative Deduction and Its Fixpoint Theory," J. Logic Programming, vol. 4, no. 1, pp. 37-53, 1986.