Reasoning with uncertainty in deductive databases and logic programs

International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems

Volumn 5, Issue 3, 1997, Pages 261-316

  Ng, Raymond T ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Deductive Databases; Dempster Shafer Formalism; Interval; Logic Programs; Reasoning with Uncertainty

Indexed keywords

EID: 3042912218     PISSN: 02184885     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218488597000245     Document Type: Article

References (72)

1. E. W. Adams, The Logic of Conditionals: An Application of Probability to Deductive Logic (Reidel, 1975).
2. E. J. Anderson and P. Nash, Linear Programming in Infinite-Dimensional Spaces: Theory and Applications (John Wiley &: Sons Ltd., 1987).
3. F. Bacchus, Representing and Reasoning with Probabilistic Knowledge (MIT Press, 1990).
4. J. F. Baldwin, "Evidential Support Logic Programming", J. of Fuzzy Sets and Systems 24 (1987) 1-26.
5. C. Bell, A. Nerode, R. Ng, and V. S. Subrahmanian, "Computation and Implementation of Non-monotonic Deductive Databases", Proc. 11th Conference on Principles of Database Systems (1992).
6. H. A. Blair and V. S. Subrahmanian, "Paraconsistent Logic Programming", Theoretical Computer Science 68 (1987) 35-54.
7. H. A. Blair and V. S. Subrahmanian, "Paraconsistent Foundations for Logic Programming", Journal of Non-Classical Logic 5 (1988) 2, 45-73.
8. G. Boolos and R. Jeffrey, Computability and Logic (Cambridge University Press, 1980).
9. R. Carnap, The Logical Foundations of Probability (University of Chicago Press, 1962).
10. P. Cheeseman, "In Defense of Probability", Proc. IJCAI-85 (1985) 1002-1009.
11. A. P. Dempster, "A Generalization of Bayesian Inference", J. of the Royal Statistical Society, Series B 30 (1968) 205-247.
12. D. Dubois and H. Prade, "Default Reasoning and Possibility Theory", Artificial Intelligence 35 (1988) 243-257.
13. D. Dubois, H. Prade, and J. Lang, (1991) "Towards Possibilistic Logic Programming", In: K. Fukurawa (ed.), Proc. 1991 Intl. Conf. on Logic Programming (MIT Press, 1991) 581-595.
14. R. O. Duda, P. E. Hart, and N. J. Nilsson, "Subjective Bayesian Methods for Rule-based Inference Systems", Proceedings of National Computer Conference (1976) 1075-1082.
15. R. Fagin and J. Halpern, "Uncertainty, Belief and Probability", Proc. IJCAI-89 (Morgan Kauffman, 1989)
16. R. Fagin, J. Y. Halpern, and N. Megiddo, "A Logic for Reasoning About Probabilities", Information and Computation (1991).
17. J. E. Fenstad, "The Structure of Probabilities Defined on First-Order Languages", In: R. C. Jeffrey (ed.), Studies in Inductive Logic and Probabilities 2 (University of California Press, 1980) 251-262.
18. M. C. Fitting, "Logic Programming on a Topological Bilattice", Fundamenta Informatica 11 (1988) 209-218.
19. M. C. Fitting, "Bilattices and the Semantics of Logic Programming", Journal of Logic Programming (1988).
20. H. Gaifman, "Concerning Measures in First Order Calculi", Israel J. of Math. 2 (1964) 1-17.
21. M. Gelfond and V. Lifschitz. (1988) "The Stable Model Semantics for Logic Programming", In: R. A. Kowalski and K. A. Bowen (eds.), Proc. 5th International Conference and Symposium on Logic Programming (1988) 1070-1080.
22. M. Ginsberg, "Multivalued Logics: A Uniform Approach to Reasoning in Artificial Intelligence", Computational Intelligence 4 (1988) 265-316.
23. B. V. Gnedenko and A. Y. Khinchin, An Elementary Introduction to the Theory of Probability (Dover Publications, 1962)
24. T. Hailperin, "Probability Logic", Notre Dame J. of Formal Logic 25 (1984) 3, 198-212.
25. M. Ishizuka, "Inference Methods Based on Extended Dempster-Shafer Theory for Problems with Uncertainty/Fuzziness", New Generation Computing 1 (1983) 2, 159-168.
26. D. Kavvadias and C. H. Papadimitriou, "A Linear Programming Approach to Reasoning About Probabilities", Annals of Mathematics and Artificial Intelligence 1 (1990) 189-205.
27. M. Kifer and A. Li, "On the Semantics of Rule-Based Expert Systems with Uncertainty", In: M. Gyssens, J. Paredaens, and D. Van Gucht (eds.), Proc. 2-nd Intl. Conf. on Database Theory, Bruges, Belgium, (Springer Verlag, 1988), Lecture Notes in Computer Science 326, 102-117.
28. M. Kifer and E. Lozinskii, "RI: A Logic for Reasoning with Inconsistency", 4-th Symposium on Logic in Computer Science, Asilomar, CA (1989) 253-262.
29. M. Kifer and V. S. Subrahmanian, "Theory of Generalized Annotated Logic Programming and its Applications", Journal of Logic Programming (1991); Preliminary version in Proc. 1989 North American Conf. on Logic Programming.
30. M. Kifer and V. S. Subrahmanian, "Theory of Generalized Annotated Logic Programming and its Applications", Journal of Logic Programming (1991); Preliminary version in Proc. 1989 North American Conf. on Logic Programming.
31. A. N. Kolmogorov, Foundations of the Theory of Probability (Chelsea Publishing Co., 1956).
32. R. Kowalski. (1974) "Predicate Logic as a Programming Language", Proc. IFIP 4 (1974) 569-574.
33. H. Kyburg, The Logical Foundations of Statistical Inference (D. Reidel, 1974).
34. V. Lifschitz, "Pointwise Circumscription", In: M. Ginzberg, Readings in Non-monotonic Reasoning (Morgan Kaufmann, 1987) 179-193.
35. J. W. Lloyd, Foundations of Logic Programming (Springer-Verlag, 1987).
36. W. Marek, A. Nerode, and J. Remmel, "A Theory of Non-Monotonic Rule Systems, Part I", Annals of Math. and AI (1993); Preliminary version in LICS-90.
37. W. Marek, A. Nerode, and J. Remmel, "A Theory of Non-Monotonic Rule Systems, Part I", Annals of Math. and AI (1993); Preliminary version in LICS-90.
38. W. Marek and V. S. Subrahmanian, (1989) "The Relationship Between Logic Program Semantics and Non-Monotonic Reasoning", Theoretical Computer Science (1992); Preliminary version in: G. Levi and M. Martelli (eds.), Proc. 6th International Conference on Logic Programming 600-617.
39. W. Marek and V. S. Subrahmanian, (1989) "The Relationship Between Logic Program Semantics and Non-Monotonic Reasoning", Theoretical Computer Science (1992); Preliminary version in: G. Levi and M. Martelli (eds.), Proc. 6th International Conference on Logic Programming 600-617.
40. W. Marek and M. Truszczynski, "Stable Semantics for Logic Programs and Default Theories", In: E. Lusk and R. Overbeek (eds.), Proc. of the 1989 North American Conference on Logic Programming (MIT Press, 1989) 243-256.
41. W. Marek and M. Truszczynski, "Relating Autoepistemic and Default Logic", In: R. Brachman, H. Levesque, and R. Reiter (eds.), Principles of Knowledge Representation and Reasoning Morgan Kaufmann, 1988) 276-288.
42. J. McCarthy, "Circumscription - a Form of Non-monotonic Reasoning", Artificial Intelligence 13 (1980) 27-39.
43. D. McDermott and J. Doyle, "Non-monotonic Logic I", Artificial Intelligence 13 (1980) 41-72.
44. R. Moore, "Semantical Considerations on Nonmonotonic Logic", Artificial Intelligence 25 (1985) 1, 75-94.
45. S. Morishita, A Unified Approach to Semantics of Multi-Valued Logic Programs (Tech. Report RT 5006, IBM Tokyo, April 9th, 1990).
46. R. T. Ng and V. S. Subrahmanian, "Probabilistic Logic Programming", Information and Computation, 101 (1992) 2, 150-201.
47. R. T. Ng and V. S. Subrahmanian, "A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases", Journal of Automated Reasoning 10 (1993) 2, 191-235; Preliminary version in Proc. 1991 International Conference of Logic Programming (1991) 565-580.
48. R. T. Ng and V. S. Subrahmanian, "A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases", Journal of Automated Reasoning 10 (1993) 2, 191-235; Preliminary version in Proc. 1991 International Conference of Logic Programming (1991) 565-580.
49. R. T. Ng and V. S. Subrahmanian, "Stable Semantics for Probabilistic Deductive Databases", Information and Computation 110 (1994) 1, 42-83.
50. R. T. Ng and V. S. Subrahmanian, "Relating Dempster-Shafer Theory to Stable Semantics", Proc. 1991 International Logic Programming Symposium (MIT Press, 1991) 551-565.
51. R. T. Ng and V. S. Subrahmanian, "Empirical Probabilities in Monadic Deductive Databases," Proceedings of 8th Conference on Uncertainty in Artificial Intelligence (1992) 215-222.
52. R. T. Ng, "Semantics and Consistency of Empirical Databases," Proceedings of 10th International Conference of Logic Programming (1993) 812-826.
53. N. Nilsson, "Probabilistic Logic", AI Journal 28 (1986) 71-87.
54. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, 1988).
55. Y. Peng and J. Reggia, "A Connectionist Model for Diagnostic Problem Solving", IEEE Trans, on Systems, Man and Cybernetics 19 (1989) 2, 285-298.
56. R. Reiter, "On Closed World Data Bases", In: Gallaire and Minker (eds.) Logic and Data Bases (1978) 55-76.
57. R. Reiter, "A Logic for Default Reasoning", Artificial Intelligence 13 (1980) 81-132.
58. R. Reiter and G. Criscuolo, "On interacting Defaults", Proc. IJCAI 81 (1981) 270-276.
59. D. S. Scott and P. Krauss, "Assigning Probabilities to Logical Formulas", In: J. Hintikka and P. Suppes (eds.), Aspects of Inductive Logic (North Holland, 1966).
60. G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, 1976).
61. G. Shafer, Dempster's Rule of Combination (unpublished manuscript, 1980).
62. E. Shapiro, "Logic Programs with Uncertainties: A Tool for Implementing Expert Systems", Proc. IJCAI'83 (M. Kauffman, 1983) 529-532.
63. J. Shoenfield, Mathematical Logic, Addison-Wesley, 1967).
64. V. S. Subrahmanian, "Mechanical Proof Procedures for Many Valued Lattice Based Logic Programming", Journal of Non-classical Logic 7 (1990) 1, 7-41.
65. V. S. Subrahmanian, "Paraconsistent Disjunctive Deductive Databases", Theoretical Computer Science 93 (1992) 115-141.
66. R. Thomason, J. Horty, and D. Touretzky, "A Calculus for Inheritance in Monotonic Semantic Nets", Proc. 2nd International Symposium on Methodologies for Intelligent Systems (1987) 280-287.
67. D. S. Touretzky, The Mathematics of Inheritance Systems (Pitman and Morgan Kaufmann, 1986).
68. M. H. van Emden, "Quantitative Deduction and its Fixpoint Theory", Journal of Logic Programming 4 (1986) 1, 137-153.
69. R. Yager, "On the Dempster-Shafer Framework and New Combination Rules", Information Sciences 41 (1987) 91-137.
70. L. A. Zadeh, "Fuzzy sets", Information and Controls (1965) 338-353.
71. L. A. Zadeh, (1968) "Fuzzy algorithms", Information and Control 12 (1968) 94-102.
72. L. A. Zadeh, "A Simple View of the Dempster-Shafer Theory of Evidence and Its Implications for the Rule of Combination", AI Magazine (1986), Summer, 85-90.