Machine Learning

, Volume 86, Issue 1, pp 3–23

ILP turns 20

Biography and future challenges
  • Stephen Muggleton
  • Luc De Raedt
  • David Poole
  • Ivan Bratko
  • Peter Flach
  • Katsumi Inoue
  • Ashwin Srinivasan
Open Access
Article

Abstract

Inductive Logic Programming (ILP) is an area of Machine Learning which has now reached its twentieth year. Using the analogy of a human biography this paper recalls the development of the subject from its infancy through childhood and teenage years. We show how in each phase ILP has been characterised by an attempt to extend theory and implementations in tandem with the development of novel and challenging real-world applications. Lastly, by projection we suggest directions for research which will help the subject coming of age.

Keywords

Inductive Logic Programming (Statistical) relational learning Structured data in Machine Learning 

References

  1. Bain, M., & Muggleton, S. H. (1991). Non-monotonic learning. In D. Michie (Ed.), Machine intelligence (Vol. 12, pp. 105–120). London: Oxford University Press. Google Scholar
  2. Blockeel, H., & De Raedt, L. (1997). Lookahead and discretisation in ILP. In N. Lavrač & S. Džeroski (Eds.), LNAI: Vol. 1297. Proceedings of the seventh international workshop on inductive logic programming (pp. 77–84). Berlin: Springer. Google Scholar
  3. Blockeel, H., De Raedt, L., Jacobs, N., & Demoen, B. (1999). Scaling up inductive logic programming by learning from interpretations. Data Mining and Knowledge Discovery, 3(1), 59–93. CrossRefGoogle Scholar
  4. Bratko, I. (2010). Discovery of abstract concepts by a robot. In LNAI: Vol. 6332. Proceedings of discovery science 2010 (pp. 372–379). Berlin: Springer. CrossRefGoogle Scholar
  5. Bratko, I., Muggleton, S. H., & Varsek, A. (1991). Learning qualitative models of dynamic systems. In Proceedings of the eighth international machine learning workshop, San Mateo, CA. San Mateo: Morgan-Kaufmann. Google Scholar
  6. Bratko, I., Leban, G., & Žabkar, J. (2008). An experiment in robot discovery with ilp. In Proceedings of the 18th international conference on inductive logic programming (ILP 2008). Berlin: Springer. Google Scholar
  7. Buntine, W. L. (1994). Operations for learning with graphical models. Journal of Artificial Intelligence Research, 2, 159–225. Google Scholar
  8. Chen, J., Muggleton, S. H., & Santos, J. (2008). Learning probabilistic logic models from probabilistic examples. Machine Learning, 73(1), 55–85. doi:10.1007/s10994-008-5076-4. CrossRefGoogle Scholar
  9. Cohen, W. (1993). PAC-learning a restricted class of logic programs. In S. Muggleton (Ed.), Proceedings of the 3rd international workshop on inductive logic programming (pp. 41–72). Google Scholar
  10. Corapi, D., Russo, A., & Lupu, E. (2010). Inductive logic programming as abductive search. In Technical communications of ICLP’10 (pp. 54–63). Google Scholar
  11. Craven, M., & Slattery, S. (2001). Relational learning with statistical predicate invention: Better models for hypertext. Machine Learning, 43(1/2), 97–119. MATHCrossRefGoogle Scholar
  12. Cussens, J. (2001). Parameter estimation in stochastic logic programs. Machine Learning, 44(3), 245–271. MATHCrossRefGoogle Scholar
  13. Davis, J., & Domingo, P. (2009). Deep transfer via second-order markov logic. In Proceedings of the twenty-sixth international workshop on machine learning (pp. 217–224). San Mateo: Morgan Kaufmann. Google Scholar
  14. De Raedt, L. (1997). Logical settings for concept-learning. Artificial Intelligence, 95(1), 197–201. Google Scholar
  15. De Raedt, L. (2008). Logical and relational learning. Berlin: Springer. MATHCrossRefGoogle Scholar
  16. De Raedt, L., & Bruynooghe, M. (1991). Clint: a multistrategy interactive concept-learner and theory revision system. In Proceedings of the 1st international workshop on multistrategy learning (pp. 175–191). San Mateo: Morgan Kaufmann. Google Scholar
  17. De Raedt, L., & Kersting, K. (2004). Probabilistic inductive logic programming. In S. Ben-David, J. Case, & A. Maruoka (Eds.), Lecture notes in computer science: Vol. 3244. Proceedings of the 15th international conference on algorithmic learning theory. Berlin: Springer. Google Scholar
  18. De Raedt, L., & Lavrač, N. (1996). Multiple predicate learning in two inductive logic programming settings. Journal on Pure and Applied Logic, 4(2), 227–254. MATHGoogle Scholar
  19. De Raedt, L., Kimmig, A., & Toivonen, H. (2007). ProbLog: a probabilistic Prolog and its application in link discovery. In R. Lopez de Mantaras & M.M. Veloso (Eds.), Proceedings of the 20th international joint conference on artificial intelligence (IJCAI-2007) (pp. 2462–2467). Google Scholar
  20. De Raedt, L., Frasconi, P., Kersting, K., & Muggleton, S. H. (Eds.) (2008). LNAI: Vol. 4911. Probabilistic inductive logic programming. Berlin: Springer. MATHGoogle Scholar
  21. Dehaspe, L., & Toivonen, H. (2001). Discovery of relational association rules. In Džeroski, S., & Lavrač, N. (Eds.), Relational data mining (pp. 189–212). Berlin: Springer. Google Scholar
  22. Dietterich, T., Domingos, P., Getoor, L., Muggleton, S. H., & Tadepalli, P. (2008). Structured machine learning: the next ten years. Machine Learning, 73(1), 3–23. doi:10.1007/s10994-008-5079-1. CrossRefGoogle Scholar
  23. Dolsak, B., & Muggleton, S. H. (1992). The application of Inductive Logic Programming to finite element mesh design. In S. H. Muggleton (Ed.), Inductive logic programming (pp. 453–472). London: Academic Press. Google Scholar
  24. Domingos, P. S., Kok, S., Poon, H., Richardson, M., & Singla, P. (2006). Unifying logical and statistical ai. In Proceedings of the twenty-first national conference on artificial intelligence, AAAI06 (pp. 2–7). Menlo Park/Cambridge: AAAI Press/MIT Press. Google Scholar
  25. Džeroski, S., & Lavrač, N. (Eds.) (2001). Relational data mining. Berlin: Springer. MATHGoogle Scholar
  26. Džeroski, S., Muggleton, S. H., & Russell, S. (1993). Learnability of constrained logic programs. In Proceedings of the European conference on machine learning (pp. 342–347). London: Springer. Google Scholar
  27. Džeroski, S., De Raedt, L., & Driessens, K. (2001). Relational reinforcement learning. Machine Learning, 43(1/2), 5–52. CrossRefGoogle Scholar
  28. Emde, W., & Wettschereck, D. (1996). Relational instance-based learning. In Proceedings of the 13th international machine learning conference (pp. 122–130). Google Scholar
  29. Esposito, F., Laterza, A., Malerba, D., & Semeraro, G. (1996). Refinement of Datalog programs. In Proceedings of the MLnet familiarization workshop on data mining with inductive logic programming (pp. 73–94). Google Scholar
  30. Feng, C. (1992). Inducing temporal fault diagnostic rules from a qualitative model. In S. H. Muggleton (Ed.), Inductive logic programming. London: Academic Press. Google Scholar
  31. Flach, P. (1993). Predicate invention in inductive data engineering. In P. B. Brazdil (Ed.), Lecture notes in artificial intelligence: Vol. 667. Machine learning: ECML-93 (pp. 83–94). Berlin: Springer. Google Scholar
  32. Flach, P. A., & Kakas, A. C. (Eds.) (2000). Abduction and induction: essays on their relation and integration. Dordrecht: Kluwer Academic. MATHGoogle Scholar
  33. Getoor, L., & Taskar, B. (Eds.) (2007). An introduction to statistical relational learning. Cambridge: MIT Press. Google Scholar
  34. Getoor, L., Friedman, N., Koller, D., & Pfeffer, A. (2001). Learning probabilistic relational models. In Džeroski, S., & Lavrač, N. (Eds.), Relational data mining (pp. 307–335). Berlin: Springer. Google Scholar
  35. Graham, J. H., Page, C. D., & Kamal, A. H. (2003). Accelerating the drug design process through parallel inductive logic programming data mining. In Proceedings of the IEEE computer society bioinformatics conference—CSB (pp. 400–402). New York: IEEE Press. CrossRefGoogle Scholar
  36. Horsch, M., & Poole, D. L. (1990). A dynamic approach to probabilistic inference using Bayesian networks. In Proc. sixth conference on uncertainty in AI, Boston, July 1990 (pp. 155–161). Google Scholar
  37. Inoue, K. (2004). Induction as consequence finding. Machine Learning, 55, 109–135. MATHCrossRefGoogle Scholar
  38. Inoue, K., Furukawa, K., Kobayashiand, I., & Nabeshima, H. (2010). Discovering rules by meta-level abduction. In L. De Raedt (Ed.), LNAI: Vol. 5989. Proceedings of the nineteenth international conference on inductive logic programming (ILP09) (pp. 49–64). Berlin: Springer. Google Scholar
  39. Kersting, K., & De Raedt, L. (2001). Towards combining inductive logic programming with bayesian networks. In LNAI: Vol. 2157. Proceedings of the eleventh international conference on inductive logic programming (pp. 118–131). Berlin: Springer. Google Scholar
  40. Kersting, K., De Raedt, L., & Raiko, T. (2006). Logical Hidden Markov Models, 25, 425–456. MATHGoogle Scholar
  41. Khardon, R. (1998). Learning first order universal Horn expressions. In Proceedings of the eleventh annual ACM conference on computational learning theory (pp. 154–165). New York: ACM. CrossRefGoogle Scholar
  42. Kietz, J. U. (1993). Some lower bounds on the computational complexity of inductive logic programming. In P. Brazdil (Ed.), Lecture notes in artificial intelligence: Vol. 667. Proceedings of the 6th European conference on machine learning (pp. 115–123). Berlin: Springer. Google Scholar
  43. King, R. D., Muggleton, S. H., Srinivasan, A., & Sternberg, M. J. E. (1996). Structure-activity relationships derived by machine learning: the use of atoms and their bond connectives to predict mutagenicity by inductive logic programming. Proceedings of the National Academy of Sciences, 93, 438–442. CrossRefGoogle Scholar
  44. King, R. D., Whelan, K. E., Jones, F. M., Reiser, P. K. G., Bryant, C. H., Muggleton, S. H., Kell, D. B., & Oliver, S. G. (2004). Functional genomic hypothesis generation and experimentation by a robot scientist. Nature, 427, 247–252. CrossRefGoogle Scholar
  45. King, R. D., Rowland, J., Oliver, S. G., Young, M., Aubrey, W., Byrne, E., Liakata, M., Markham, M., Pir, P., Soldatova, L. N., Aparkes, A., Whelan, K. E., & Clare, A. (2009). The automation of science. Science, 324(5923), 85–89. CrossRefGoogle Scholar
  46. Knobbe, A. J., Siebes, A., & Marseille, B. (2002). Involving aggregate functions in multi-relational search. In Proceedings of the 6th European conference on data mining principles and practice of knowledge discovery in databases (p. 1). Google Scholar
  47. Kramer, S., Lavrač, N., & Flach, P. (2001). Propositionalization approaches to relational data mining. In S. Džeroski & N. Lavrač (Eds.), Relational data mining (pp. 262–291). Berlin: Springer. Google Scholar
  48. Krogel, M.-A., & Wrobel, S. (2001). Transformation-based learning using multirelational aggregation. In LNCS: Vol. 2157. Inductive logic programming (pp. 142–155). CrossRefGoogle Scholar
  49. Landwehr, N., Kersting, K., & De Raedt, L. (2007). Integrating naive Bayes and Foil. Journal of Machine Learning Research, 8, 481–507. MATHGoogle Scholar
  50. Lavrač, N., & Džeroski, S. (1993). Inductive logic programming: techniques and applications. Chichester: Ellis Horwood. Google Scholar
  51. Lavrač, N., Džeroski, S., & Grobelnik, M. (1991). Learning non-recursive definitions of relations with LINUS. In Y. Kodratoff (Ed.), Lecture notes in artificial intelligence: Vol. 482. Proceedings of the 5th European working session on learning. Berlin: Springer. Google Scholar
  52. Lisi, F. A., & Malerba, D. (2003). Bridging the gap between horn clausal logic and description logics in inductive learning. In LNCS: Vol. 2829. AI*IA 2003: Advances in artificial intelligence. Berlin: Springer. Google Scholar
  53. Lloyd, J. W. (2003). Logic for learning. Berlin: Springer. MATHGoogle Scholar
  54. Mihalkova, L., & Mooney, R. J. (2009). Transfer learning from minimal target data by mapping across relational domains. In IJCAI-09: Proceedings of the twentieth international joint conference on artificial intelligence (pp. 1163–1168). San Mateo: Morgan-Kaufmann. Google Scholar
  55. Milch, B., Zettlemoyer, L. S., Kersting, K., Haimes, M., & Kaelbling, L. P. (2008). Lifted probabilistic inference with counting formulas. In Proceedings of the twenty third conference on artificial intelligence (AAAI). Google Scholar
  56. Morik, K., Wrobel, S., Kietz, J., & Emde, W. (1993). Knowledge acquisition and machine learning: theory, methods and applications. London: Academic Press. Google Scholar
  57. Moyle, S., & Muggleton, S. H. (1997). Learning programs in the event calculus. In N. Lavrač & S. Džeroski (Eds.), LNAI: Vol. 1297. Proceedings of the seventh inductive logic programming workshop (ILP97) (pp. 205–212). Berlin: Springer. Google Scholar
  58. Muggleton, S. H. (1987). Duce, an oracle based approach to constructive induction. In IJCAI-87 (pp. 287–292). Los Altos: Kaufmann. Google Scholar
  59. Muggleton, S. H. (1991). Inductive logic programming. New Generation Computing, 8(4), 295–318. MATHCrossRefGoogle Scholar
  60. Muggleton, S. H. (Ed.) (1992). Inductive logic programming. San Diego: Academic Press. MATHGoogle Scholar
  61. Muggleton, S. H. (1995). Inverse entailment and Progol. New Generation Computing, 13, 245–286. CrossRefGoogle Scholar
  62. Muggleton, S. H. (1996). Stochastic logic programs. In L. de Raedt (Ed.), Advances in inductive logic programming (pp. 254–264). Amsterdam: IOS Press. Google Scholar
  63. Muggleton, S. H. (2002). Learning structure and parameters of stochastic logic programs. In Proceedings of the 12th international conference on inductive logic programming (pp. 198–206). Berlin: Springer. Google Scholar
  64. Muggleton, S. H., & Bryant, C. H. (2000). Theory completion using inverse entailment. In Proc. of the 10th international workshop on inductive logic programming (ILP-00) (pp. 130–146). Berlin: Springer. Google Scholar
  65. Muggleton, S. H., & Buntine, W. (1988). Machine invention of first-order predicates by inverting resolution. In Proceedings of the 5th international conference on machine learning (pp. 339–352). Los Altos: Kaufmann. Google Scholar
  66. Muggleton, S. H., & De Raedt, L. (1994). Inductive logic programming: Theory and methods. Journal of Logic Programming, 19–20, 629–679. CrossRefGoogle Scholar
  67. Muggleton, S. H., & Feng, C. (1990). Efficient induction of logic programs. In Proceedings of the first conference on algorithmic learning theory (pp. 368–381). Tokyo: Ohmsha. Google Scholar
  68. Muggleton, S. H., & Feng, C. (1992). Efficient induction of logic programs. In S. H. Muggleton (Ed.), Inductive logic programming (pp. 281–298). London: Academic Press. Google Scholar
  69. Muggleton, S. H., King, R. D., & Sternberg, M. J. E. (1992). Protein secondary structure prediction using logic-based machine learning. Protein Engineering, 5(7), 647–657. CrossRefGoogle Scholar
  70. Muggleton, S. H., Fidjeland, A., & Luk, W. (2002). Scalable acceleration of inductive logic programs. In IEEE international conference on field-programmable technology (pp. 252–259). New York: IEEE Press. Google Scholar
  71. Nienhuys-Cheng, S.-H., & de Wolf, R. (1997). LNAI: Vol. 1228. Foundations of inductive logic programming. Berlin: Springer. Google Scholar
  72. Otero, R. (2005). Induction of the indirect effects of actions by monotonic methods. In Proceedings of the fifteenth international conference on inductive logic programming (ILP05) (Vol. 3625, pp. 279–294). Berlin: Springer. Google Scholar
  73. Passerini, A., Frasconi, P., & De Raedt, L. (2006). Kernels on Prolog proof trees: statistical learning in the ILP setting. Journal of Machine Learning Research, 7, 307–342. MATHGoogle Scholar
  74. Plotkin, G. D. (1969). A note on inductive generalisation. In B. Meltzer & D. Michie (Eds.), Machine intelligence (Vol. 5, pp. 153–163). Edinburgh: Edinburgh University Press. Google Scholar
  75. Plotkin, G. D. (1971a). Automatic methods of inductive inference. Ph.D. thesis, Edinburgh University, August 1971. Google Scholar
  76. Plotkin, G. D. (1971b). A further note on inductive generalization. In Machine intelligence (Vol. 6). Edinburgh: Edinburgh University Press. Google Scholar
  77. Poole, D. L. (1991). Representing diagnostic knowledge for probabilistic Horn abduction (pp. 1129–1135). Sydney. Google Scholar
  78. Poole, D. L. (1993). Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence, 64(1), 81–129. MATHCrossRefGoogle Scholar
  79. Poole, D. L. (1997). The independent choice logic for modelling multiple agents under uncertainty. Artificial Intelligence, 94, 7–56. Special issue on economic principles of multi-agent systems. MATHMathSciNetCrossRefGoogle Scholar
  80. Poole, D. L. (2000). Abducing through negation as failure: stable models within the independent choice logic. Journal of Logic Programming, 44(1–3), 5–35. MATHMathSciNetCrossRefGoogle Scholar
  81. Poole, D. L. (2003). First-order probabilistic inference. In Proc. eighteenth international joint conference on artificial intelligence (IJCAI-03), Acapulco, Mexico (pp. 985–991). Google Scholar
  82. Poole, D. L. (2008). The independent choice logic and beyond. In L. De Raedt, P. Frasconi, K. Kersting, & S. Muggleton (Eds.), LNCS: Vol. 4911. Probabilistic inductive logic programming: theory and application. Berlin: Springer. Google Scholar
  83. Poole, D. L., & Mackworth, A. K. (2010). Artificial intelligence: foundations of computational agents. New York: Cambridge University Press. MATHCrossRefGoogle Scholar
  84. Quinlan, J. R. (1987). Generating production rules from decision trees. In Proceedings of the tenth international conference on artificial intelligence (pp. 304–307). Los Altos: Kaufmann. Google Scholar
  85. Quinlan, J. R. (1990). Learning logical definitions from relations. Machine Learning, 5, 239–266. Google Scholar
  86. Quinlan, J. R., & Cameron-Jones, R.M. (1993). FOIL: a midterm report. In P. Brazdil (Ed.), Lecture notes in artificial intelligence: Vol. 667. Proceedings of the 6th European conference on machine learning (pp. 3–20). Berlin: Springer. Google Scholar
  87. Ray, O., Broda, K., & Russo, A. (2003). Hybrid abductive inductive learning: a generalisation of Progol. In Lecture notes in artificial intelligence: Vol. 2835. Proceedings of the 13th international conference on inductive logic programming (ILP’03) (pp. 311–328). Berlin: Springer. Google Scholar
  88. Richardson, M., & Domingos, P. (2006). Markov logic networks. Machine Learning, 62, 107–136. CrossRefGoogle Scholar
  89. Rouveirol, C., & Puget, J.-F. (1989). A simple and general solution for inverting resolution. In EWSL-89 (pp. 201–210). London: Pitman. Google Scholar
  90. Russell, S. J., & Norvig, P. (2010). Artificial intelligence: a modern approach (3rd ed.). New Jersey: Pearson. Google Scholar
  91. Sammut, C., & Banerji, R.B. (1986). Learning concepts by asking questions. In R. Michalski, J. Carbonnel, & T. Mitchell (Eds.), Machine learning: an artificial intelligence approach (Vol. 2, pp. 167–192). Los Altos: Kaufmann. Google Scholar
  92. Sammut, C., & Webb, G. (Eds.) (2010). Encyclopedia of machine learning. Berlin: Springer. Google Scholar
  93. Sanner, S., & Kersting, K. (2010). Symbolic dynamic programming. In C. Sammut & G. Webb (Eds.), Encyclopedia of machine learning. Berlin: Springer. Google Scholar
  94. Santos Costa, V., Page, D., Qazi, M., & Cussens, J. (2003). CLP(BN): Constraint logic programming for probabilistic knowledge. In Proceedings of the 19th conference on uncertainty in artificial intelligence (pp. 517–524). Google Scholar
  95. Sato, T. (2005). Generative modeling with failure in prism. In International joint conference on artificial intelligence (pp. 847–852). San Mateo: Morgan Kaufmann. Google Scholar
  96. Sato, T., & Kameya, Y. (1997). PRISM: a symbolic-statistical modeling language. In Proceedings of the 15th international joint conference on artificial intelligence (IJCAI-97) (pp. 1330–1335). Google Scholar
  97. Sato, T., & Kameya, Y. (2008). New advances in logic-based probabilistic modeling by PRISM. In L. De Raedt, P. Frasconi, K. Kersting, & S. Muggleton (Eds.), LNCS: Vol. 4911. Probabilistic inductive logic programming (pp. 118–155). Berlin: Springer. CrossRefGoogle Scholar
  98. Shapiro, E. Y. (1983). Algorithmic program debugging. Cambridge: MIT Press. Google Scholar
  99. Stahl, I. (1992). Constructive induction in inductive logic programming: an overview (Technical report). Fakultat Informatik, Universitat Stuttgart. Google Scholar
  100. Stahl, I. (1996). Predicate invention in inductive logic programming. In L. De Raedt (Ed.), Advances in inductive logic programming (pp. 34–47). Amsterdam: IOS Press. Google Scholar
  101. Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning: an introduction. Cambridge: MIT Press. Google Scholar
  102. Synnaeve, G., Inoue, K., Doncescu, A., Kameya, Y., Sato, T., Ishihata, M., & Nabeshima, H. (2011). Kinetic models and qualitative abstraction for relational learning in systems biology. In Proceedings of the international conference on bioinformatics models, methods and algorithms. Google Scholar
  103. Tamaddoni-Nezhad, A., Chaleil, R., Kakas, A., & Muggleton, S. H. (2006). Application of abductive ILP to learning metabolic network inhibition from temporal data. Machine Learning, 64, 209–230. doi:10.1007/s10994-006-8988-x. MATHCrossRefGoogle Scholar
  104. Tamaddoni-Nezhad, A., Chaleil, R., Kakas, A., Sternberg, M. J. E., Nicholson, J., & Muggleton, S. H. (2007). Modeling the effects of toxins in metabolic networks. IEEE Engineering in Medicine and Biology, 26, 37–46. doi:10.1109/MEMB.2007.335590. CrossRefGoogle Scholar
  105. Torrey, L., & Shavlik, J. W. (2010). Policy transfer via Markov logic networks. In L. De Raedt (Ed.), LNAI: Vol. 5989. Proceedings of the nineteenth international conference on inductive logic programming (ILP09) (pp. 234–248). Berlin: Springer. Google Scholar
  106. Van den Broeck, G., Thon, I., van Otterlo, M., & De Raedt, L. (2010). DTProbLog: A decision-theoretic probabilistic prolog. In Proceedings of the AAAI conference on artificial intelligence (AAAI 2010). Google Scholar
  107. van Otterlo, M. (2009). The logic of adaptive behavior—knowledge representation and algorithms for adaptive sequential decision making under uncertainty in first-order and relational domains. Amsterdam: IOS Press. MATHGoogle Scholar
  108. Vens, C., Ramon, J., & Blockeel, H. (2006). Refining aggregate conditions in relational learning. In J. Fürnkranz, T. Scheffer, & M. Spiliopoulou (Eds.), Lecture notes in computer science: Vol. 4213. Proceedings of the 10th European conference on principles and practice of knowledge discovery in databases (pp. 383–394). Berlin: Springer. Google Scholar
  109. Vere, S. A. (1975). Induction of concepts in the predicate calculus. In Proceedings of the 4th international joint conference on artificial intelligence (pp. 282–287). San Mateo: Morgan Kaufmann. Google Scholar
  110. Wrobel, S. (1994). Concept formation during iterative theory revision. Machine Learning, 14, 169–191. MATHMathSciNetCrossRefGoogle Scholar
  111. Yamamoto, Y., Inoue, K., & Iwanuma, K. (2010). From inverese entailment to inverese subsumption. In Proceedings of the 20th international conference on inductive logic programming (ILP’10). Google Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Stephen Muggleton
    • 1
  • Luc De Raedt
    • 2
  • David Poole
    • 3
  • Ivan Bratko
    • 4
  • Peter Flach
    • 5
  • Katsumi Inoue
    • 6
  • Ashwin Srinivasan
    • 7
  1. 1.Imperial College LondonLondonUK
  2. 2.Katholieke Universiteit LeuvenLeuvenBelgium
  3. 3.University of British ColumbiaVancouverCanada
  4. 4.University of LjubljanaLjubljanaSlovenia
  5. 5.University of BristolBristolUK
  6. 6.National Institute of InformaticsTokyoJapan
  7. 7.South Asian UniversityNew DelhiIndia

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