On computing all abductive explanations from a propositional Horn theory

Journal of the ACM

Volumn 54, Issue 5, 2007, Pages

  Eiter, Thomas ^a   Makino, Kazuhisa ^b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

Abduction; Characteristic set; Dualization problem; Enumeration algorithms; Horn theories; Model based reasoning; NP hardness; Polynomial total time computation; Prime implicates; Propositional logic; Tractability

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; POLYNOMIALS; QUERY PROCESSING;

ABDUCTION; CHARACTERISTIC SET; DUALIZATION PROBLEMS; ENUMERATION ALGORITHMS; HORN THEORIES; MODEL BASED REASONING; NP HARDNESS; POLYNOMIAL TOTAL-TIME COMPUTATION; PRIME IMPLICATES; PROPOSITIONAL LOGIC;

ARTIFICIAL INTELLIGENCE;

EID: 35348939165     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1284320.1284323     Document Type: Article

References (76)

1. ANGLUIN, D. 1987. Learning prepositional Horn sentences with hints. Tech. Rep. Yale/DCS/RR-590, Dept. of Computer Science, Yale University.
2. APT, K., AND BEZEM, M. 1991. Acyclic programs. New Gen. Comput. 9, 3-4, 335-364.
3. ARIMURA, H. 1997. Learning acyclic first-order Horn sentences from entailment. In Proceedings 7th International Workshop on Algorithmic Learning Theory (ALT'97), M. Li and A. Maruoka, Eds. Lecture Notes in Computer Science, vol. 1316. Springer, 432-445.
4. BIOCH, C., AND IBARAKI, T. 1995. Complexity of identification and dualization of positive Boolean functions. Info. Comput. 123, 50-63.
5. BOROS, E., CEPEK, O., AND KOGAN, A. 1998. Horn minimization by iterative decomposition. Ann. Math. Artif. Intel. 23, 3-4, 321-343.
6. BOROS, E., CRAMA, Y., AND HAMMER, P. L. 1990. Polynomial-time inference of all valid implications for Horn and related formulae. Ann. Math. Artif. Intel. 1, 21-32.
7. BREWKA, G., DIX, J., AND KONOLIGE, K. 1997. Nonmonotonic Reasoning - An Overview. Number 73 in CSLI Lecture Notes. CSLI Publications, Stanford University, Stanford, CA.
8. BSHOUTY, N. H. 1995. Exact learning Boolean functions via the monotone theory. Inf. Comput. 123, 146-153.
9. BYLANDER, T. 1991. The monotonic abduction problem: A functional characterization on the edge of tractability. In Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR-91). 70-77.
10. CONSOLE, L., SAPINO, M.L., AND THESEIDER DUPRÉ, D. 1995. The role of abduction in database view updating. J. Intel. Inf. Syst. 4, 3, 261-680.
11. CONSOLE, L., THESEIDER DUPRÉ, D., AND TORASSO, P. 1991. On the relationship between abduction and deduction. J. Logic Comput. 1, 5, 661-690.
12. DE KLEER, J. 1986. An assumption-based truth maintenance system. Artif. Intel. 28, 127-162.
13. DECHTER, R., AND PEARL, J. 1992. Structure identification in relational data. Artif. Intel. 58, 237-270.
14. DEL VAL, A. 1999. A new method for consequence finding and compilation in restricted languages. In Proceedings of the 16th American National Conference on Artificial Intelligence (AAAI'99). AAAI Press/The MIT Press, Cambridge, MA, 259-264.
15. DEL VAL, A. 2000a. On some tractable classes in deduction and abduction. Artif. Intel. 116, 1-2, 297-313.
16. DEL VAL, A. 2000a. The complexity of restricted consequence finding and abduction. In Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI-2000). AAAI Press/The MIT Press, Cambridge, MA, 337-342.
17. DOWLING, W., AND GALLIER, J. H. 1984. Linear-time algorithms for testing the satisfiability of propositional Horn theories. J. Logic Prog. 3, 267-284.
18. DOWNEY, R. G., FELLOWS, M., AND FELLOWS, M. 1998. Parameterized Complexity. Springer-Verlag, New York.
19. EITER, T., AND GOTTLOB, G. 1991. Identifying the minimal transversals of a hypergraph and related problems. Tech. Rep. CD-TR 91/16, Christian Doppler Laboratory for Expert Systems, TU Vienna, Austria. January.
20. (Shortened version in SIAM J. Comput., 24(6): 1278-1304, 1995).
21. EITER, T., AND GOTTLOB, G. 1995. The complexity of logic-based abduction. J. ACM 42, 1 (Jan.), 3-42.
22. EITER, T., GOTTLOB, G., AND LEONE, N. 1997. Abduction from logic programs: Semantics and complexity. Theoret. Comput. Sci. 189, 1-2 (Dec), 129-177.
23. EITER, T., GOTTLOB, G., AND MAKINO, K. 2002. New results on monotone dualization and generating hypergraph transversals. In Proceedings of the 34th ACM Symposium on Theory of Computing (STOC 2002). ACM, New York, 14-22.
24. (Full paper SIAM J. Computing, 32(2):514-537, 2003.)
25. EITER, T., AND MAKINO, K. 2002. On computing all abductive explanations. In Proceedings of the 18th National Conference on Artificial Intelligence (AAAI '02). AAAI Press, 62-67.
26. EITER, T., AND MAKINO, K. 2003a. Abduction and the dualization problem. In Proceedings of the 6th International Conference on Discovery Science (DS 2003), Sapporo, Japan., Oct. 17-19, G. Grieser, Y. Tanaka, and A. Yamamoto, Eds. Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence, vol. 2843. Springer-Verlag, New York, 1-20.
27. EITER, T., AND MAKINO, K. 2003b. Generating all abductive explanations for queries on propositional Horn theories. In Proceedings 12th Annual Conference of the EACSL (CSL 2003), (Vienna, Austria, Aug. 25-30) M. Baaz and J. Makowsky, Eds. Lecture Notes in Computer Science, vol. 2803, Springer-Verlag, New York, 197-211.
28. EITER, T., MAKINO, K., AND GOTTLOB, G. 2007. Computational aspects of monotone dualization: A brief survey. Discrete Applied Mathematics, doi:10.1016/j.dam.2007.04.017.
29. EKIN, O., HAMMER, P. L., AND KOGAN, A. 1999. On connected Boolean functions. Disc. Appl. Math. 96-97, 337-362.
30. ESHGHI, K. 1993. A tractable class of abduction problems. In Proceedings IJCAI-93 (Chambery, France), Morgan. Kaufmann, San Francisco, CA, 3-8.
31. FAGIN, R. 1982. Horn clauses and database dependencies. J. ACM 29, 952-985.
32. FREDMAN, M., AND KHACHIYAN, L. 1996. On the complexity of dualization of monotone disjunctive normal, forms. J. Algorithms 21, 618-628.
33. FRIEDRICH, G., GOTTLOB, G., AND NEIDL, W. 1990. Hypothesis classification, abductive diagnosis, and therapy. In Proceedings of the International Workshop on Expert Systems in Engineering. Lecture Notes in Artificial Intelligence, vol. 462, Springer-Verlag, New York, 69-78.
34. GINSBERG, M. L. 1988. Knowledge-base reduction: A new approach to checking knowledge bases for inconsistency & redundancy. In Proceedings of the 7th National Conference on Artificial Intelligence (AAAI-88). AAAI Press, 585-589.
35. GOLDSMITH, J., AND SLOAN, R. 2005. New Horn revision algorithms. J. Mach. Learn. Res. 6, 1919-1938.
36. GOLDSMITH, J., SLOAN, R. H., SZÖRÉ NYI, B., AND TURÁN, G. 2004. New revision algorithms. In Proceedings 15th International Conference on Algorithmic Learning Theory (ALT 2004), S. Ben-David, J. Case, and A. Maruoka, Eds. Lecture Notes in Computer Science, vol. 3244. Springer-Verlag, New York, 395-409.
37. GOTTLOB, G., PICHLER, R., AND WEI, F. 2006. Bounded treewidth as a key to tractability of knowledge representation and reasoning. In Proceedings of the 21th National Conference on Artificial Intelligence (AAAI '06). AAAI Press.
38. GOTTLOB, G., SCARCELLO, F., AND SIDERI, M. 2002. Fixed parameter complexity in AI and nonmonotonic reasoning. Artif. Intel. 138, 1-2, 55-86.
39. HAMMER, P., AND KOGAN, A. 1992. Horn functions and their DNFs. Inf. Proc. Lett. 44, 23-29.
40. HAMMER, P., AND KOGAN, A. 1995. Quasi-acyclic propositional Horn knowledge bases: Optimal compression. IEEE Trans. Knowl. Data Engi. 7, 5, 751-762.
41. HAMMER, P. L., AND KOGAN, A. 1994. Graph-based methods for Horn knowledge compression. In Proceedings of the 27th Hawaii International Conference on System Sciences, (HICSS'94). IEEE, 300-309.
42. IBARAKI, T., KOGAN, A., AND MAKINO, K. 2003. Inferring minimal functional dependencies in Horn and q-Horn theories. Ann. Math. Artif. Intel. 38, 4, 233-255.
43. INOUE, K. 1992. Linear resolution for consequence finding. Artif. Intel. 56, 2-3, 301-354.
44. JOHNSON, D. S. 1990. A catalog of complexity classes. In Handbook of Theoretical Computer Science, J. van Leeuwen, Ed. Vol. A. Elsevier Science Publishers B.V. (North-Holland), Chap. 2.
45. KAKAS, A., KOWALSKI, R., AND TONI, F. 1998. The role of abduction in logic programming. In Handbook of Logic in Artificial Intelligence and Logic Programming, D. M. Gabbay, C. J. Hogger, and J. A. Robinson, Eds. Vol. V: Logic Programming. Clarendon Press, Oxford, UK, 235-324.
46. KAUTZ, H., KEARNS, M., AND SELMAN, B. 1993. Reasoning with characteristic models. In Proceedings of the 11th National Conference on Artificial Intelligence (AAAI-93). AAAI Press, 34-39.
47. KAUTZ, H., KEARNS, M., AND SELMAN, B. 1995. Horn approximations of empirical data. Artif. Intel. 74, 129-245.
48. KAVVADIAS, D., PAPADIMTTRIOU, C., AND SIDERI, M. 1993. On Horn envelopes and hypergraph transversals. In Proceedings 4th International Symposium on Algorithms and Computation (ISAAC-93), W. Ng, Ed. Lecture Notes in Computer Science, vol. 762. Springer-Verlag, New York, 399-405.
49. 2n]. Inf. Proc. Lett. 85, 1-6.
50. KEAN, A., AND TSIKNIS, G. 1990. An incremental method for generating prime implicants. J. Symb. Comput. 9, 185-206.
51. KEAN, A., AND TSIKNIS, G. 1992a. Assumption based reasoning and clause management systems. Comput. Intell. 8, 1, 1-24.
52. KEAN, A., AND TSIKNIS, G. 1992b. Clause management systems (CMS). Comput. Intell. 9, 1, 11-40.
53. KHARDON, R. 1995. Translating between Horn representations and their characteristic Models. J. Artif. Intell. Res. 3, 349-372.
54. KHARDON, R., MANNILA, H., AND ROTH, D. 1999. Reasoning with examples: Propositional formulae and database dependencies. Acta Inform. 36, 4, 267-286.
55. KHARDON, R., AND ROTH, D. 1996. Reasoning with models. Artif. Intell. 87, 1/2, 187-213.
56. KHARDON, R., AND ROTH, D. 1997. Defaults and relevance in model-based reasoning. Artif. Intell. 97, 1/2, 169-193.
57. LEVESQUE, H. 1986. Making believers out of computers. Artif. Intell. 30, 81-108.
58. LONC, Z., AND TRUSZCZYŃSKI, M. 2003. Fixed-parameter complexity of semantics for logic programs. ACM Trans. Comput. Logic 4, 1, 91-119.
59. LUCCHESI, C. L., AND OSBORN, S. 1978. Candidate keys for relations. J. Comput. Syst. Sci. 17, 270-279.
60. MAKOWSKY, J. 1987. Why Horn formulas matter for computer science: initial structures and generic examples. J. Comput. Syst. Sci. 34, 2/3, 266-292.
61. MANNILA, H., AND RÄIHÄ, K.-J. 1986. Design by example: An application of Armstrong relations. J. Comput. Syst. Sci. 22, 2, 126-141.
62. MANNILA, H., AND RÄIHÄ, K.-J. 1988. Algorithms for inferring functional dependencies. Tech. Rep. A-1988-3, University of Tampere, Dept. of Comput Science, Series of Publ. A. April.
63. MARQUIS, P. 2000. Consequence finding algorithms. In Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. V: Algorithms for Uncertainty and Defeasible Reasoning. D. Gabbay and Ph.Smets, Eds. Kluwer Academic, 41-145.
64. MCKINSEY, J. 1943. The decision problem for some classes of sentences without quantifiers. J. Symb. Logic 8, 61-76.
65. NGUYEN, T. A., PERKINS, W. A., LAFFEY, T. J., AND PECORA, D. 1987. Knowledge-base verification. AI Magazine 8, 2, 69-75.
66. PAPADMITRIOU, C. H. 1994. Computational Complexity. Addison-Wesley. Reading, MA.
67. POOLE, D. 1989. Explanation and prediction: An architecture for default and abductive reasoning. Comput. Intel. 5, 1, 97-110.
68. PROVAN, G. 1990. The computational complexity of multiple-context truth maintenance systems. In Proceedings of the ECAI-90. 522-527.
69. REDDY, C., AND TADEPALLI, P. 1998. Learning first-order acyclic Horn programs from entailment. In Proceedings of the 15th International Conference on Machine Learning (ICML 1998), J. W. Shavlik, Ed. Morgan Kaufmann, San Francisco, CA, 472-480.
70. REITER, R., AND DE KLEER, J. 1982. Foundations of assumption-based truth maintenance systems: Preliminary report. In Proceedings of the 6th National Conference on Artificial Intelligence (AAAI-87). AAAI Press, 183-188.
71. RUTENBURG, V. 1991. Complexity classification in truth maintenance systems. In Proceedings STACS-91. vol. 480, Lecture Notes in Computer Science. Springer-Verlag, New York, pp. 373-383.
72. (Full paper In Annal. Math. Artif. Intel., 10:207-231, 1994.
73. SELMAN, B., AND LEVESQUE, H. J. 1990. Abductive and default reasoning: A computational core. In Proceedings of the 8th National Conference on Artificial Intelligence (AAAI-90). AAAI Press, 343-348.
74. SELMAN, B., AND LEVESQUE, H. J. 1996. Support set selection for abductive and default reasoning. Artif. Intell. 82, 259-272.
75. VALIANT, L. G., AND VAZIRANI, V. V. 1986. NP is as easy as detecting unique solutions. Theoret. Comput. Sci. 47, 1, 85-93.
76. ZANUTTINI, B. 2003. New polynomial classes for logic-based abduction. J. Artif. Intell. Res. 19, 1-10.