×

zbMATH — the first resource for mathematics

An ILP model for a monotone graded classification problem. (English) Zbl 1249.68265
Summary: The motivation for this paper are classification problems in which data cannot be clearly divided into positive and negative examples, especially data in which there is a monotone hierarchy (degree, preference) of more or less positive (negative) examples. We present a new formulation of a fuzzy inductive logic programming task in the framework of fuzzy logic in the narrow sense. Our construction is based on a syntactical equivalence of fuzzy logic programs FLP and a restricted class of generalised annotated programs. The induction is achieved via multiple use of the classical two-valued induction on \(\alpha \)-cuts of fuzzy examples with monotonicity axioms in background knowledge, which is afterwards again glued together to a single annotated hypothesis. Correctness of our method (translation) is based on the correctness of FLP. The cover relation is based on fuzzy Datalog and fixpoint semantics for FLP. We present and discuss results of the ILP systems GOLEM and ALEPH on illustrative examples. We comment on relations of our results to some statistical models and Bayesian logic programs.
MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
03B70 Logic in computer science
03B50 Many-valued logic
68N17 Logic programming
Software:
FOIL
PDF BibTeX XML Cite
Full Text: Link EuDML
References:
[1] Andrejková G., Jirásek J.: Neural network topologies and evolutionary design. Neural Network World 6 (2001), 547-560
[2] Bouchon-Meunier B., Marsala, Ch.: Improvement of the interpretability of fuzzy rules constructed by means of fuzzy decision tree based systems. Abstracts of FSTA 2002, Liptovský Ján, Slovakia 2002
[3] Drobics M., Bodenhofer, U., Winiwarter W.: Interpretation of self-organizing maps with fuzzy rules. ICTAI 2000, IEEE
[4] Džeroski S., Lavrač N.: An introduction to inductive logic programming. Relational Data Mining (S. Džeroski and N. Lavrač Springer-Verlag, Berlin 2001, pp. 48-73
[5] al L. Getoor et: Learning probabilistic relational models. Relational Data Mining (S. Džeroski and N. Lavrač, Springer-Verlag, Berlin 2001, pp. 307-335 · Zbl 0989.68551
[6] Hájek P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht 1999 · Zbl 1007.03022
[7] Jenčušová E., Jirásek J.: Formal methods of security protocols. Tatra Mt. Math. Publ. 25 (2002), 1-10 · Zbl 1049.68056
[8] Kersting K., Raedt L. De: Towards combining Inductive Logic Programming with Bayesian Networks. Proc. ILP 2001 (C. Rouveirol and M. Sebagh, Lecture Notes in Artificial Intelligence 2157), Springer-Verlag, Berlin 2001, pp. 118-131 · Zbl 1006.68518 · link.springer.de
[9] Kersting K., Raedt L. De: Adaptive Bayesian Logic Programs. Proc. ILP 2001 (C. Rouveirol and M. Sebagh, Lecture Notes in Artificial Intelligence 2157), Springer-Verlag, Berlin 2001, pp. 104-117 · Zbl 1006.68504 · link.springer.de
[10] Kifer M., Subrahmanian V. S.: Theory of generalized anotated logic programming and its applications. J. Logic Programming 12 (1992), 335-367 · doi:10.1016/0743-1066(92)90007-P
[11] Klose A., Nürnberger A., Nauck, D., Kruse R.: Data Mining with Neuro-Fuzzy Models. Data Mining and Computational Intelligence (A. Kandel, H. Bunke, and M. Last, Physica-Verlag, Heidelberg 2001, pp. 1-36
[12] Krajči S., Lencses, R., Vojtáš P.: A data model for annotated programs. ADBIS’02-Research Com. (Y. Manolopoulos and P. Návrat, Vydavatelstvo STU, Bratislava 2002, pp. 141-154
[13] Krajči S., Lencses, R., Vojtáš P.: A comparison of fuzzy and annotated logic programming. Fuzzy Sets and Systems 144 (2004), 173-192 · Zbl 1065.68024 · doi:10.1016/j.fss.2003.10.019
[14] Lin C.-T., Lee C.-C.: Neural Fuzzy Systems. A Neuro-Fuzzy Synergism to Intelligent Systems. Prentice Hall, New York 1996
[15] Muggleton S.: Inductive logic programming. New Gen. Comp. 8 (1991), 295-318 · Zbl 0712.68022 · doi:10.1007/BF03037089
[16] Muggleton S.: Inverse entailment and Progol. New Gen. Comp. 13 (1995), 245-286 · Zbl 05479869 · doi:10.1007/BF03037227
[17] Nauck D., Klawonn, F., Kruse R.: Foundations of Neuro-Fuzzy Systems. Wiley, Chichester 1997 · Zbl 1086.68109
[18] Quinlan J. R.: Learning logical definitions from relations. Mach. Learning 5 (1990), 239-266 · doi:10.1007/BF00117105
[19] Quinlan J. R., Cameron-Jones R. M.: FOIL: A midterm report. Proc. 6th European Conference on Machine Learning (P. Brazdil, Lecture Notes in Artificial Intelligence 667), Springer-Verlag, Berlin 1993, pp. 3-20
[20] Raedt L. De, Džeroski S.: First order jk-clausal theories are PAC-learnable. Artificial Intelligence 70 (1994), 375-392 · Zbl 0938.68773 · doi:10.1016/0004-3702(94)90112-0
[21] al D. Shibata et: An induction algorithm based on fuzzy logic programming. Proc. PAKDD’99 (Ning Zhong and Lizhu Zhou, Lecture Notes in Computer Science 1574), Springer-Verlag, Berlin 1999, pp. 268-273
[22] Vojtáš P.: Fuzzy logic programming. Fuzzy Sets and Systems 124 (2001), 361-370 · Zbl 1015.68036 · doi:10.1016/S0165-0114(01)00106-3
[23] Železný F.: Learning functions from imperfect positive data. Proc. ILP 2001 (C. Rouveirol and M. Sebag, Lecture Notes in Computer Science 2157), Springer-Verlag, Berlin 2001, pp. 248-259 · Zbl 1006.68512 · link.springer.de
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.