Was the Year 2000 a Leap Year? Step-Wise Narrowing Theories with Metagol

  • Michael SiebersEmail author
  • Ute Schmid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11105)


Many people believe that every fourth year is a leap year. However, this rule is too general: year X is a leap year if X is divisible by 4 except if X is divisible by 100 except if X is divisible by 400. We call such a theory with alternating generalisation and specialisation a step-wise narrowed theory. We present and evaluate an extension to the ILP system Metagol which facilitates learning such theories. We enabled Metagol to learn over-general theories by allowing a limited number of false positives during learning. This variant is iteratively applied on a learning task. For each iteration after the first, positive examples are the false positives from the previous iteration and negative examples are the true positives from the previous iteration. Iteration continues until no more false positives are present. Then, the theories are combined to a single step-wise narrowed theory. We evaluate the usefulness of our approach in the leap year domain. We can show that our approach finds solutions with fewer clauses, higher accuracy, and in shorter time.


Step-wise narrowed theory Metagol Over-generalization 



We like to thank Andrew Cropper for valuable discussions on negation in Metagol. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SCHM 1239/10-1.


  1. 1.
    Richards, E.G.: Calendars. In: Urban, S.E., Seidelmann, P.K. (eds.) Explanatory Supplement to the Astronomical Almanac, pp. 585–624 (2013)Google Scholar
  2. 2.
    Quinlan, J.R.: Induction of decision trees. Mach. Learn. 1, 81–106 (1986)Google Scholar
  3. 3.
    Mitchell, T.M.: Machine Learning. McGraw-Hill, New York (1997)zbMATHGoogle Scholar
  4. 4.
    Muggleton, S., Buntine, W.: Machine invention of first-order predicates by inverting resolution. In: Machine Learning Proceeding, pp. 339–352 (1988),
  5. 5.
    Bain, M., Muggleton, S.: Non-monotonic Learning. In: Machine Intelligence 12 - Towards an Automated Logic of Human Thought, pp. 105–120 (1991)Google Scholar
  6. 6.
    Malerba, D., Esposito, F., Lisi, F.A.: Learning Recursive Theories with ATRE. In: ECAI (European Conference on Artificial Intelligence), pp. 435–439 (1998)Google Scholar
  7. 7.
    Malerba, D.: Learning recursive theories in the normal ILP setting. Fundamenta Informaticae 57, 39–77 (2003)Google Scholar
  8. 8.
    Ray, O.: Nonmonotonic abductive inductive learning. J. Appl. Logic 7, 329–340 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Stahl, I.: Predicate Invention in ILP - an Overview. In: Machine Learning: ECML-1993, pp. 313–322 (1993)Google Scholar
  10. 10.
    Muggleton, S.H., Lin, D., Pahlavi, N., Tamaddoni-Nezhad, A.: Meta-interpretive learning: application to grammatical inference. Mach. Learn. 94, 25–49 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lin, D., Dechter, E., Ellis, K., Tenenbaum, J., Muggleton, S.H.: Bias reformulation for one-shot function induction. In: ECAI (European Conference on Artificial Intelligence), pp. 525–530 (2014).
  12. 12.
    Cropper, A., Muggleton, S.H.: Learning higher-order logic programs through abstraction and invention. In: IJCAI (International Joint Conference on Artificial Intelligence), pp. 1418–1424 (2016)Google Scholar
  13. 13.
    Muggleton, S.H., Lin, D., Tamaddoni-Nezhad, A.: Meta-interpretive learning of higher-order dyadic datalog: predicate invention revisited. Mach. Learn. 100, 49–73 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Cropper, A., Muggleton, S.H.: Metagol System (2016).
  15. 15.
    Larson, J., Michalski, R.S.: Inductive Inference of VL Decision Rules. ACM SIGART Bull., 38–44, June 1977Google Scholar
  16. 16.
    Siebers, M., Schmid, U., Seuß, D., Kunz, M., Lautenbacher, S.: Characterizing facial expressions by grammars of action unit sequences - a first investigation using ABL. Inf. Sci. 329, 866–875 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Cognitive SystemsUniversity of BambergBambergGermany

Personalised recommendations