Inferring Minimal Functional Dependencies in Horn and q-Horn Theories

Authors:
Toshihide Ibaraki;Alexander Kogan;Kazuhisa Makino
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501 E-mail: ibaraki@i.kyoto-u.ac.jp;Department of Accounting and Information Systems, Rutgers Business School, Rutgers University, Newark, NJ 07102, and RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854-8003, US ...;Division of Systems Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan 560-8531 E-mail: makino@sys.es.osaka-u.ac.jp
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2003

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Abstract

In this paper, we study various problems related to the inference of minimal functional dependencies in Horn and q-Horn theories. We show that if a Horn theory is represented by a Horn CNF, then there exists an incrementally polynomial algorithm for inferring all minimal functional dependencies. On the other hand, if a Horn theory is represented as the Horn envelope of a given set of models, then there exists a polynomial total time algorithm for this inference problem if and only if there exists such an algorithm for dualizing a positive CNF. Finally, we generalize our results to the case of q-Horn theories, and show that all the considered problems can be reduced in polynomial time to the corresponding problems for Horn theories.