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On the complexity of some inductive logic programming problems

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Abstract

The bounded ILP-consistency problem for function-free Horn clauses is described as follows. Given at setE + andE − of function-free ground Horn clauses and an integerk polynomial inE +∪E −, does there exist a function-free Horn clauseC with no more thank literals such thatC subsumes each element inE + andC does not subsume any element inE −? It is shown that this problem is Σ P2 complete. We derive some related results on the complexity of ILP and discuss the usefulness of such complexity results.

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Authors and Affiliations

  1. Institut für Informationssysteme, Technische Universität Wien, Paniglgasse 16, A-1040, Wien, Austria

    Georg Gottlob & Nicola Leone

  2. Istituto per la Sistemistica e l’Informatica (ISI-CNR) c/o DEIS, Università della Calabria, I-87036, Rende (CS), Italy

    Francesco Scarcello

Authors
  1. Georg Gottlob
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  2. Nicola Leone
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  3. Francesco Scarcello
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Corresponding author

Correspondence to Georg Gottlob.

Additional information

Georg Gottlob, Ph.D.: He is a Professor of Computer Science at the Technical University of Vienna, Austria, where he currently chairs the department of Information Systems and the Database and Artificial Intelligence Lab. His research interests are logic programming, database theory (in particular, query languages), nonmonotonic reasoning, finite model theory, and computational complexity. He has extensively published in all these areas. On the more applied side, he supervises a number of industry projects dealing with expert systems and with multimedia information systems. Dr. Gottlob holds his current position since 1988. Before that, he was affiliated with the Italian National Research Council in Genoa, Italy, and before with the Politecnico di Milano, Italy. He has lectured at Stanford University and in various European universities. He is Editor-in-Chief of AI-Communications and on the editorial board of various other journals and he served as Program Committee co-chair of several conferences, e.g. the 1998 Symposium of Computer Science Logic.

Nicola Leone: He received the italian Laurea degree in Mathematics from the University of Calabria. In June 1986 he joined CRAI (an industrial consortium for computer science research and application at Rende, Italy), where he worked until December 91. From January 1992 to September 1995, he has been with the ISI institute of CNR (the Italian National Research Council). Since October 1995, he is Professor for Database Systems at the Information Systems Department of the Vienna University of Technology. Nicola Leone has partecipated to several national and international projects mainly on the development of advanced Data and Knowledge Bases, including the ESPRIT projects “KIWIS” and “EDS” (where he acted as the leader of the CRAI team). Currently, he is the leader of an FWF project on the implementation of a Disjunctive Deductive Database System. His main research interests are in the areas of Database Theory, Non-Monotonic Reasoning, Complexity Theory, and Deductive Databases. He is author of over eighty papers published in conference proceedings, books, and scientific journals, including alsoInformation and Computation, AI Journal, ACM Transactions, IEEE Transactions, TCS, JLP, andNGC.

Francesco Scarcello, Ph.D.: He received a Ph. D. in “Ingegneria dei Sistemi e Informatica” from University of Calabria (Italy) in 1997. Since 1996 he is recipient of a grant from ISI-CNR (Istituto per la Sistemistica e l’Informatica, Consiglio Nazionale delle Ricerche). Recently, he spent one year at at the Information Systems Department of the Vienna University of Technology as a visiting scientist. His present research interests include knowledge representation, nonmonotonic reasoning, logic programming, computational complexity, database theory, approximation of logical theories, and inductive logic programming.

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Gottlob, G., Leone, N. & Scarcello, F. On the complexity of some inductive logic programming problems. New Gener Comput 17, 53–75 (1999). https://doi.org/10.1007/BF03037582

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  • DOI: https://doi.org/10.1007/BF03037582

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