Functional dependencies in Horn theories

Artificial Intelligence

Volumn 108, Issue 1, 1999, Pages 1-30

  Ibaraki, Toshihide ^a   Kogan, Alexander ^b,c   Makino, Kazuhisa ^d  

^a KYOTO UNIVERSITY   (Japan)

^b RUTGERS UNIVERSITY   (United States)

^c RUTGERS UNIVERSITY   (United States)

^d OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; POLYNOMIALS; PROBLEM SOLVING;

ACYCLIC DIRECTED GRAPH; CONJUNCTIVE NORMAL FORM; FUNCTIONAL DEPENDENCIES; HORN THEORIES;

KNOWLEDGE REPRESENTATION;

EID: 0033620270     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0004-3702(98)00114-3     Document Type: Article

References (44)

1. [1] W.W. Armstrong, Dependency structures of database relationships, in: Proceedings IFIP-74, North-Holland, Amsterdam, 1974, pp. 580-583.
2. [2] C. Beeri, M. Dowd, R. Fagin, R. Statman, On the structure of Armstrong relations for functional dependencies, J. ACM 31 (1) (1984) 30-46.
3. [3] J.C. Bioch, T. Ibaraki, Complexity of identification and dualization of positive Boolean functions, Inform. and Comput. 123 (1995) 51-75.
4. [4] E. Boros, Y. Crama, P.L. Hammer, Polynomial time inference of all valid implications for Horn and related formulae, Ann. Math. Artificial Intelligence 1 (1990) 21-32.
5. [5] E. Boros, Y. Crama, P.L. Hammer, M. Saks, A complexity index for satisfiability problems, SIAM J. Comput. 23 (1994) 45-49.
6. [6] E. Boros, O. Čepek, A. Kogan, Horn minimization by iterative decomposition, Ann. Math, and Artificial Intelligence 23 (3-4) (1998) 321-343.
7. [7] E. Boros, P.L. Hammer, X. Sun, Recognition of q-Horn formulae in linear time, Discrete Appl. Math. 55 (1994) 1-13.
8. [8] V. Chandru, C.R. Coullard, P.L. Hammer, M. Montañez, X. Sun, On renamable Horn and generalized Horn functions, Ann. Math. Artificial Intelligence 1 (1990) 33-47.
9. [9] C.L. Chang, R.C.T. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.
10. [10] E.F. Codd, A relational model for large shared data banks, Comm. ACM 13 (1970) 377-387.
11. [11] R. Dechter, J. Pearl, Structure identification in relational data, Artificial Intelligence 58 (1992) 237-270.
12. [12] C. Delobel, R.G. Casey, Decomposition of a data base and the theory of Boolean switching functions, IBM J. Res. Development 17 (1973) 374-386.
13. [13] W.F. Dowling, J.H. Gallier, Linear time algorithms for testing the satisfiability of propositional Horn formulae, J. Logic Programming 3 (1984) 267-284.
14. [14] R. Fagin, Functional dependencies in a relational database and propositional logic, IBM J. Res. Development 21 (1977) 534-544.
15. [15] R. Fagin, Horn clauses and database dependencies, J. ACM 29 (4) (1982) 952-985.
16. [16] M.R. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA, 1979.
17. [17] P.L. Hammer, A. Kogan, Horn functions and their DNFs, Inform. Process. Lett. 44 (1992) 23-29.
18. [18] P.L. Hammer, A. Kogan, Optimal compression of propositional Horn knowledge bases: Complexity and approximation, Artificial Intelligence 64 (1993) 131-145.
19. [19] P.L. Hammer, A. Kogan, Quasi-acyclic propositional Horn knowledge bases: Optimal compression, IEEE Trans. Knowledge and Data Engineering 7 (1995) 751-762.
20. [20] P.L. Hammer, A. Kogan, Essential and redundant rules in Horn knowledge bases, Decision Support Systems 16 (2) (1996) 119-130.
21. [21] A. Horn, On sentences which are true of direct unions of algebras, J. Symbolic Logic 16 (1951) 14-21.
22. [22] T. Ibaraki, A. Kogan, K. Makino, Functional dependencies in Horn theories, RUTCOR Research Report RRR 14-98, Rutgers University, New Brunswick, NJ, 1998.
23. [23] T. Ibaraki, A. Kogan, K. Makino, Functional dependencies in q-Horn theories, Manuscript, 1998.
24. [24] H. Kautz, M. Kearns, B. Selman, Horn approximations of empirical data, Artificial Intelligence 74 (1995) 129-145.
25. [25] H. Kautz, M. Kearns, B. Selman, Forming concepts for fast inference, in: Proc. AAAI-92, San Jose, CA, 1992, pp. 786-793.
26. [26] D. Kavvadias, C.H. Papadimitriou, M. Sideri, On Horn envelopes and hypergraph transversals, in: K.W. Ng et al. (Eds.), Algorithms and Computation - ISAAC-93, Lecture Notes in Computer Science, Vol. 762, Springer, Berlin, 1993, pp. 399-405.
27. [27] R. Khardon, Translating between Horn representations and their characteristic models, J. Artificial Intelligence Res. 3 (1995) 349-372.
28. [28] R. Khardon, H. Mannila, D. Roth, Reasoning with examples: Propositional formulae and database dependencies, Acta Informatica (1998) to appear. (Preliminary version: Technical Report TR-15-95, Aiken Computation Laboratory, Harvard University, Cambridge, MA, 1995.)
29. [29] R. Khardon, D. Roth, Reasoning with models, Artificial Intelligence 87 (1996) 187-213.
30. [30] J. Kivinen, H. Mannila, Approximate inference of functional dependencies from relations, Theoret. Comput. Sci. 149 (1995) 129-149.
31. [31] H.R. Lewis, Renaming a set of clauses as a Horn set, J. ACM 25 (1978) 134-135.
32. [32] C.L. Lucchesi, S.L. Osborn, Candidate keys for relations, J. Comput. System Sci. 17 (1978) 270-279.
33. [33] D. Maier, The Theory of Relational Databases, Computer Science Press, Rockville, MD, 1983.
34. [34] H. Mannila, K.-J. Räihä, Design of Relational Databases, Addison-Wesley, Wokingham, 1992.
35. [35] H. Mannila, K.-J. Räihä, Algorithms for inferring functional dependencies, Data and Knowledge Engineering 12 (1994) 83-99.
36. [36] J.C.C. McKinsey, The decision problem for some classes of sentences without quantifiers, J. Symbolic Logic 8 (3) (1943) 61-77.
37. [37] M. Minoux, LTUR: A simplified linear-time unit resolution algorithm for Horn formulae and computer implementation, Inform. Process. Lett. 29 (1988) 1-12.
38. [38] M. Minoux, The unique Horn-Satisfiability problem and quadratic Boolean equations, Ann. Math. Artificial Intelligence 6 (1992) 253-266.
39. [39] Y. Sagiv, C. Delobel, D.S. Parker, R. Fagin, An equivalence between relational database dependencies and a fragment of prepositional logic, J. ACM 28 (3) (1981) 435-453.
40. [40] B. Selman, H. Kautz, Knowledge compilation and theory approximation, J. ACM 43 (2) (1996) 193-224.
41. [41] B. Selman, H.J. Levesque, Support set selection for abductive and default reasoning, Artificial Intelligence 82 (1996) 259-272.
42. [42] J.D. Ullman, Principles of Database and Knowledge-Base Systems, Vol. I: Classical Database Systems, Computer Science Press, New York, 1988.
43. [43] J.D. Ullman, Principles of Database and Knowledge-Base Systems, Vol. II: The New Technologies, Computer Science Press, New York, 1989.
44. [44] Yu.I. Zhuravlev, A. Kogan, Realization of Boolean functions with a small number of zeros by disjunctive normal forms and related problems, Soviet Mathematics - Doklady 32 (3) (1985) 771-775.