Horn extensions of a partially defined boolean function

SIAM Journal on Computing

Volumn 28, Issue 6, 1999, Pages 2168-2186

  Makinq, Kazuhisa ^a   Hatanaka, Ken Ichi ^b   Ibaraki, Toshihide ^c  

^a OSAKA UNIVERSITY   (Japan)

^b SUMITOMO ELECTRIC INDUSTRIES LTD   (Japan)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

Extension; Horn function; Knowledge acquisition; Partially defined boolean function

Indexed keywords

KNOWLEDGE ACQUISITION; POLYNOMIALS; SET THEORY; VECTORS;

DISJUNCTIVE NORMAL FORM (DNF); HORN EXTENSIONS; PARTIALLY DEFINED BOOLEAN FUNCTIONS (PDBF); TRUE BOOLEAN VECTORS;

BOOLEAN FUNCTIONS;

EID: 0033147348     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0097539796297954     Document Type: Article

References (25)

1. D. ANGLUIN, M. FRAZIER, AND L. PITT, Learning conjunctions of Horn clauses, Mach. Learning, 9 (1992), pp. 147-164.
2. E. BORGS, V. GURVICH, P. L. HAMMER, T. IBARAKI, AND A. KOGAN, Decompositions of partially defined Boolean functions, Discrete Appl. Math., 62 (1995), pp. 51-75.
3. J. C. BIOCII AND T. IBARAKI, Complexity of identification and dualization of positive Boolean functions, Inform, and Comput., 123 (1995), pp. 50-63.
4. E. BOROS, T. IBARAKI, AND K. MAKING, Error-free and best-fit extensions of partially defined Boolean functions, Inform, and Comput., 140 (1998), pp. 254-283.
5. S. CEFU, G. GOTTLOB, AND L. TANCA, Logic Programming and Databases, Springer, Berlin, New York, 1990.
6. Y. CRAMA, P. L. HAMMER, AND T. IBARAKI, Cause-effect relationships and partially defined Boolean functions, Ann. Oper. Res., 16 (1988), pp. 299-326.
7. D. W. DOWLING AND J. H. GALLIER, Linear-time algorithms for testing the satisfying ofpropo- sitional Horn formulae, J. Logic Programming, 3 (1984), pp. 267-284.
8. R. DECHTER AND J. PEARL, Structure identification in relational data, Artificial Intelligence, 58 (1992), pp. 237-270.
9. T. ElTER AND G. GOTTLOB, Identifying the minimal transversals of a hypergraph and related problems, SIAM J. Comput., 24 (1995), pp. 1278-1304.
10. M. FREDMAN AND L. KHACHIYAN, On the complexity of dualization of monotone disjunctive normal forms, J. Algorithms, 21 (1996), pp. 618-628.
11. M. R. GAREY AND D. S. JOHNSON, Computers and Intractability, Freeman, New York, 1979.
12. M. GOLUMBIC, P. L. HAMMER, P. HANSEN, AND T. IBARAKI, EDS., Horn Logic, Search and Satisfiability, Ann. Math. Artificial Intelligence, 1 (1990), no. 1-4, Baltzer Science Publishers BV, Amsterdam, 1990.
13. P. L. HAMMER AND A. KOGAN, Optimal compression of propositional Horn knowledge bases: Complexity and approximation, Artificial Intelligence, 64 (1993), pp. 131-145.
14. P. L. HAMMER AND A. KOGAN, Horn functions and their DNFs, Inform. Process. Lett., 44 (1992), pp. 23-29.
15. A. HORN, On sentences which are true of direct unions of algebras, J. Symbolic Logic, 16 (1951), pp. 14-21.
16. D. S. JOHNSON, M. YANNAKAKIS, AND C. H. PAPADIMITRIOU, On generating all maximal independent sets, Inform. Process. Lett., 27 (1988), pp. 119-123.
17. H. A. KAUTZ, M. J. KEARNS, AND B. SELMAN, Horn approximations of empirical data, Artificial Intelligence, 74 (1995), pp. 129-145.
18. D. KAVVADIAS, C. H. PAPADIMITRIOU, AND M. SIDERI, On Horn envelopes and hypergraph transversals, in ISAAC'93, Algorithms and Computation, K. W. Ng et al., eds., Lecture Notes in Comput. Sei. 762, Springer, Berlin, 1993, pp. 399-405.
19. R. KHARDON, Translating between Horn representations and their characteristic models, J. rtificial Intelligence Res., 3 (1995), pp. 349-372.
20. K. MAKING, K. YANO, AND T. IBARAKI, Positive and Horn decomposability of partially defined Boolean functions, Discrete Appl. Math., 74 (1997), pp. 251-274.
21. J. C. C. McKlNSEY, The decision problem for some classes of sentences without quantifiers, J. Symbolic Logic, 8 (1943), pp. 61-76.
22. D. PRETOLANI, A linear time algorithm for unique Horn satisfiability, Inform. Process. Lett., 48 (1993), pp. 61-66.
23. W. QuiNE, A way to simplify truth functions, Amer. Math. Monthly, 62 (1955), pp. 627-631.
24. J. R. QUINLAN, Induction of decision trees, Mach. Learning, 1 (1986), pp. 81-106.
25. B. SELMAN AND H. KAUTZ, Knowledge compilation using Horn approximations, in Proceedings f the Ninth National Conference on Artificial Intelligence (AAAI-91), July 14-19, 1991, Anaheim, ÇA, Amer. Assoc. Artif. Intell., Menlo Park, CA, 1991, pp. 904-909.