The Well-Founded Semantics for General Logic Programs

Journal of the ACM (JACM)

Volumn 38, Issue 3, 1991, Pages 619-649

  Van Gelder, Allen ^a   Ross, Kenneth A ^b   Schlipf, John S ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITY OF CINCINNATI   (United States)

Author keywords

fixpoints; negation as failure; stable models; three valued logic; unfounded sets; well founded models

Indexed keywords

EID: 84976799999     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/116825.116838     Document Type: Article

References (43)

1. APT, K. R., BLAIR, H., AND WALKER, A. Towards a theory of declarative knowledge. In J. Minker, ed. Foundations of Deductive Databases and Logic Programming. Morgan-Kaufmann, San Mateo, Calif., 1988, pp. 89-148.
2. APT, K. R., AND VAN EMDEN, M. H. Contributions to the theory of logic programming. J. ACM 29, 3 (July 1982), 841-862.
3. BRY, F. Logic programming as constructivism: A formalization and its application to databases. In Proceedings of the 8th ACM Symposium on Principles of Database Systems. ACM, New York, pp. 34-50.
4. CHANDRA, A., AND HAREL, D. Structure and complexity of relational queries. J. Comput. Syst. Sci. 25, 1 (1982), 99-128.
5. CHANDRA, A., AND HAREL, D. Horn clause queries and generalizations. J. Logic Prog. 2, 1 (1985), 1-15.
6. CLARK, K. L. Negation as failure. In H. Gallaire and J. Minker, eds., Logic and Databases. Plenum Press, New York, 1978, pp. 293-322.
7. DUMMETT, M. A. E. Elements of Intuitionism. Clarendon Press, Oxford, England, 1977.
8. DUNG, PH. M., AND KANCHANASUT, K. A natural semantics for logic programs with negation. Tech. Rep. Asian Institute of Technology, Bangkok 10501, Thailand, 1989. (manuscript).
9. FITTING, M. A Kripke-Kleene semantics for logic programs. J. Logic Progr. 2, 4 (1985) 295-312.
10. GELFOND, M. On stratified autoepistemic theories. In Proceedings of the 6th National Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, Calif., 1987, pp. 207-211.
11. GELFOND, M, AND LIFSCHITZ, V. The stable model semantics for logic programming. In Proceedings of the 5th International Conference and Symposium on Logic Programming (Seattle, Wash.). IEEE, New York, 1988, pp. 1070-1080.
12. GUREVICH, Y., AND SHELAH S. Fixed-point extensions of first order logic. Ann. Pure Appl. Logic 32 (1986), 265-280.
13. HANKS, S., AND MCDERMOTT, D. Default reasoning, nonmonotonic logics, and the frame problem. In Proceedings of 5th National Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, Calif., 1986, pp. 328-333.
14. IMMERMAN, N. Relational queries computable in polynomial time. Inf. Contr. 68, 1 (1986), 86-104.
15. JAFFAR, J., LASSEZ, J.-L., AND LLOYD, J. Completeness of the negation-as-failure rule. In Proceedings of the International Joint Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, Calif., 1983, pp. 500-506.
16. KOLAITIS, P. G. The expressive power of stratified programs. Inf. Comput. 90 1 (1991), 50-66.
17. KUNEN, K. Negation in logic programming. J. Logic Prog. 4, 4 (1987), 289-308.
18. KUNEN, K. Some remarks on the completed database. Tech. Rep. 775. Univ. of Wisconsin, Madison, Wisc., 1988. (Abstract appeared in Proceedings of the 5th International Conference and Symposium on Logic Programming (Seattle, Wash., Aug.) 1988).
19. LIFSCHITZ, V. On the declarative semantics of logic programs with negation. In J. Minker, ed. Foundations of Deductive Databases and Logic Programming. Morgan-Kaufmann, San Mateo, Calif., 1988, pp. 172-192.
20. LLOYD, J. W. Foundations of Logic Programming. Springer-Verlag, New York, 2nd edition, 1987.
21. LLOYD, J. W., AND TOPOR, R. W. Making Prolog more expressive. J. Logic Prog. 1. 3 (1984), 225-240.
22. MAHER, M. J. Equivalences of logic programs. In J. Minker, ed. Foundations of Deductive Databases and Logic Programming. Morgan-Kaufmann, San Mateo, Calif., 1988, pp. 388-402.
23. MAREK, W. Stable theories in autoepistemic logic. Tech. Rep., Univ. Kentucky, Lexington, Ky., 1986.
24. MAREK, A., AND TRUSZCZYNSKI, M. Autoepistemic logic. Tech. Rep., Univ. Kentucky, Lexington, Ky., 1988.
25. MINKER, J. On indefinite databases and the closed world assumption. In Proceedings of the 6th Conference on Automated Deduction. Springer-Verlag, New York, 1982, pp. 292-308.
26. MOORE, R. C. Semantical considerations on nonmonotonic logic. Artif. Int. 28 (1985). 75-94.
27. MORRIS, K. Talk at Workshop XP8.3i, Oregon Graduate Center, July 1987.
28. MORRIS, K., ULLMAN, J. D., AND VAN GELDER, A. Design overview of the Nail! system. In Proceedings of the 3rd International Conference on Logic Programming. 1986, pp. 554-568.
29. MOSCHOVAKIS, Y. N. Elementary Induction on Abstract Structures. North-Holland, New York, 1974.
30. PRZYMUSINSKA, H, AND PRZYMUSINSKI, T. C. Weakly perfect model semantics for logic programs. In Proceedings of the 5th International Conference and Symposium on Logic Programming (Seattle, Wash.), 1988, pp. 1106-1120.
31. PRZYMUSINSKI, T. C. On the declarative semantics of deductive databases and logic programs. In J. Minker, ed. Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Mateo, Calif., 1988, pp. 193-216.
32. PRZYMUSINSKI, T. C. Every logic program has a natural stratification and an iterated fixed point model. In Proceedings of the 8th ACM Symposium on Principles of Database Systems. ACM, New York, 1989, pp. 11-21.
33. REITER, R. On closed world databases. In H. Gallaire and J. Minker, Logic and Databases. Plenum Press, New York, 1978, pp. 55-76.
34. Ross, K. A., A procedural semantics for well-founded negation in logic programs. In Proceedings of the 8th ACM Symposium on Principles of Database Systems. ACM, New York, 1989, pp. 22-33.
35. Ross, K., AND TOPOR. R. W. Inferring negative information from disjunctive databases. J. Autom. Reas. 4 (1988), 397-424.
36. SCHLIPF, J. S. Negation by securable failure in logic programming. Unpublished manuscript, 1987.
37. SHEPHERDSON, J. C. Negation as failure, II. J. Logic Prog. 2, 3 (1985), 185-202.
38. SHEPHERDSON, J. C. Negation in logic programming. In J. Minker, ed., Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Mateo, Calif., 1988, pp. 19-88.
39. VAN EMDEN, M. H., AND KOWALSKI, R. A. The semantics of predicate logic as a programming language. J. ACM 23, 4 (Oct. 1976), 733-742.
40. VAN GELDER, A. Negation as failure using tight derivations for general logic programs. J. Logic Prog., 6, 1 (1989), 109-133. (Preliminary versions appeared in Proceedings of the 3rd IEEE Symposium on Logic Programming, IEEE, New York, 1986, and Foundations of Deductive Databases and Logic Programming, J. Minker, ed., Morgan Kaufmann, San Mateo, Calif., 1988.
41. VAN GELDER, A. Modeling simultaneous events with default reasoning and tight derivations. J. Logic Prog. 8, 1 (1990), 41-52.
42. VAN GELDER, A. The alternating fixpoint of logic programs with negation. J. Comput. Syst. Sci. 1992, to appear. (Available as Tech. Rep. UCSC-CRL-89-39, Preliminary abstract appeared in Proceedings of the 8th Annual ACM Symposium on Principles of Database Systems. ACM, New York, 1989.)
43. VARDI, M. The complexity of relational query languages. In Proceedings of the 14th ACM Symposium on Theory of Computing. ACM, New York, 1982, pp. 137-145.