Learning Stochastic Logical Automaton

  • Hiroaki Watanabe
  • Stephen Muggleton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4012)


This paper is concerned with algorithms for the logical generalisation of probabilistic temporal models from examples. The algorithms combine logic and probabilistic models through inductive generalisation. The inductive generalisation algorithms consist of three parts. The first part describes the graphical generalisation of state transition models. State transition models are generalised by applying state mergers. The second part involves symbolic generalisation of logic programs which are embedded in each states. Plotkin’s LGG is used for symbolic generalisation of logic programs. The third part covers learning of parameters using statistics derived from the input sequences. The state transitions are unobservable in our settings. The probability distributions over the state transitions and actions are estimated using the EM algorithm. As an application of these algorithms, we learn chemical reaction rules from StochSim, the stochastic software simulator of biochemical reactions.


Logic Program Logical State Belief State Inductive Logic Inductive Logic Programming 


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  1. 1.
    McCarthy, J., Hayes, P.J.: Some Philosophical Problems from the Standpoint of Artificial Intelligence. In: Machine Intelligence, vol. 4, pp. 463–502. Edinburgh University Press (1969)Google Scholar
  2. 2.
    Rabiner, L.: A tutorial on hidden markov models and selected applications in speech recognition. Proceedings of the IEEE 77 (1989)Google Scholar
  3. 3.
    Watanabe, H., Muggleton, S.: First-Order Stochastic Action Language. Electronic Transactions in Artificial Intelligence 7 (2002), http://www.doc.ic.ac.uk/~hw3/doc/watanabe02FirstSAL.ps
  4. 4.
    H. Watanabe, S. Muggleton.: Towards Belief Propagation in Shared Logic Program, BN2003, Kyoto (2003), http://www.doc.ic.ac.uk/~hw3/doc/bn2003final2.pdf
  5. 5.
    Moyle, S., Muggleton, S.H.: Learning programs in the event calculus. In: Džeroski, S., Lavrač, N. (eds.) ILP 1997. LNCS (LNAI), vol. 1297, pp. 205–212. Springer, Heidelberg (1997)Google Scholar
  6. 6.
    Otero, R.: Induction of Stable Models. In: Rouveirol, C., Sebag, M. (eds.) ILP 2001. LNCS (LNAI), vol. 2157, pp. 193–205. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Kersting, K., Raiko, T., De Raedt, L.: Logical Hidden Markov Models (Extended Abstract). In: Ga’mez, J.A., Salmero’n, A. (eds.) Proceedings of the First European Workshop on Probabilistic Graphical Models (PGM-02), Cuenca, Spain, November 6-8, 2002, pp. 99–107 (2002)Google Scholar
  8. 8.
    Kersting, K., De Raedt, L.: Logical markov decision programs and the convergence of logical TD(λ). In: Camacho, R., King, R., Srinivasan, A. (eds.) ILP 2004. LNCS, vol. 3194, pp. 180–197. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Morton-Firth, C.J.: Stochastic simulation of cell signalling pathways Ph.D. Thesis, University of Cambridge (1998)Google Scholar
  10. 10.
    Dupont, P., Miclet, L., Vidal, E.: What is the search space of Regular Inference? In: Carrasco, R.C., Oncina, J. (eds.) ICGI 1994. LNCS (LNAI), vol. 862, pp. 25–37. Springer, Heidelberg (1994)Google Scholar
  11. 11.
    Coste, F., Fredouille, D.: What is the search space for the inference of non deterministic, unambiguous and deterministic automata? technical report INRIA RR-4907 (2003)Google Scholar
  12. 12.
    Plotkin, G.: Automatic Methods of Inductive Inference. PhD thesis, Edinburgh University, UK (1971)Google Scholar
  13. 13.
    Gold, E.M.: Complexity of automaton identification from given data. Information and Control 37(3), 302–320 (1978)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Angluin, D.: Negative Results for Equivalence Queries. Machine Learning 5, 121–150 (1990)Google Scholar
  15. 15.
    Kearns, M., Valiant, L.G.: Cryptographic limitations on learning boolean formulae and finite automata. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pp. 433–444. ACM Press, New York (1989)Google Scholar
  16. 16.
    Angluin, D.: Learning regular sets from queries and counterexamples. Information and Computation 75, 87–106 (1987)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Halpern, J.Y.: An analysis of first-order logics of probability. In: Proceedings of IJCAI-1989, 11th International Joint Conference on Artificial Intelligence, pp. 1375–1381 (1989)Google Scholar
  18. 18.
    Muggleton, S.H.: Stochastic logic programs. In: de Raedt, L. (ed.) Advances in Inductive Logic Programming, pp. 254–264. IOS Press, Amsterdam (1996)Google Scholar
  19. 19.
    Taisuke Sato.: A statistical learning method for logic programs with distribution semantics. Proc. ICLP 1995, Syounan-village, pages 715–729, 1995.Google Scholar
  20. 20.
    Kersting, K., Raedt, L.D.: Bayesian Logic Programs. In: Cussens, J., Frisch, A.M. (eds.) ILP 2000. LNCS (LNAI), vol. 1866, pp. 138–155. Springer, Heidelberg (2000)Google Scholar
  21. 21.
    Friedman, N., Getoor, L., Koller, D., Pfeffer, A.: Learning probabilistic relational models. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, pp. 1300–1309. Morgan Kaufmann Publishers, San Francisco (1999)Google Scholar
  22. 22.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice-Hall, Englewood Cliffs (2003)Google Scholar
  23. 23.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)MATHGoogle Scholar
  24. 24.
    Kietz, J.-U., Lübbe, M.: An efficient subsumption algorithm for inductive logic programming. In: Proc. of the 4th International Workshop on Inductive Logic Programming (ILP-1994), pp. 97–105 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hiroaki Watanabe
    • 1
  • Stephen Muggleton
    • 1
  1. 1.Imperial College LondonLondonUK

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