Logic for Programming, Artificial Intelligence, and Reasoning

Logic for Programming, Artificial Intelligence, and Reasoning pp 88-96 | Cite as

FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9450)

Abstract

FEMaLeCoP is a connection tableau theorem prover based on leanCoP which uses efficient implementation of internal learning-based guidance for extension steps. Despite the fact that exhaustive use of such internal guidance can incur a significant slowdown of the raw inferencing process, FEMaLeCoP trained on related proofs can prove many problems that cannot be solved by leanCoP. In particular on the MPTP2078 benchmark, FEMaLeCoP adds 90 (15.7 %) more problems to the 574 problems that are provable by leanCoP. FEMaLeCoP is thus the first AI/ATP system convincingly demonstrating that guiding the internal inference algorithms of theorem provers by knowledge learned from previous proofs can significantly improve the performance of the provers. This paper describes the system, discusses the technology developed, and evaluates the system.

References

  1. 1.
    Alama, J., Heskes, T., Kühlwein, D., Tsivtsivadze, E., Urban, J.: Premise selection for mathematics by corpus analysis and kernel methods. J. Autom. Reasoning 52(2), 191–213 (2014)CrossRefGoogle Scholar
  2. 2.
    Blanchette, J.C., Kaliszyk, C., Paulson, L.C., Urban, J.: Hammering towards QED. J. Formalized Reasoning (2015, in press)Google Scholar
  3. 3.
    Carlson, A., Cumby, C., Rosen, J., Roth, D.: The SNoW learning architecture. Technical report UIUCDCS-R-99-2101, UIUC Computer Science (1999)Google Scholar
  4. 4.
    Gauthier, T., Kaliszyk, C.: Matching concepts across HOL libraries. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS, vol. 8543, pp. 267–281. Springer, Heidelberg (2014) Google Scholar
  5. 5.
    Ibens, O., Letz, R.: Subgoal alternation in model elimination. In: Galmiche, D. (ed.) TABLEAUX 1997. LNCS, vol. 1227, pp. 201–215. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  6. 6.
    Jones, K.S.: A statistical interpretation of term specificity and its application in retrieval. J. Documentation 28, 11–21 (1972)CrossRefGoogle Scholar
  7. 7.
    Kaliszyk, C., Urban, J.: Stronger automation for Flyspeck by feature weighting and strategy evolution. In: Blanchette, J.C., Urban, J. (eds.) PxTP 2013. EPiC Series, vol. 14, pp. 87–95. EasyChair (2013)Google Scholar
  8. 8.
    Kaliszyk, C., Urban, J.: MizAR 40 for Mizar 40. J. Autom. Reasoning 55, 245–256 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kaliszyk, C., Urban, J., Vyskocil, J.: Efficient semantic features for automated reasoning over large theories. In: Yang, Q., Wooldridge, M. (eds.) IJCAI 2015, pp. 3084–3090. AAAI Press (2015)Google Scholar
  10. 10.
    Kaliszyk, C., Urban, J., Vyskočil, J.: Certified connection tableaux proofs for HOL Light and TPTP. In: Leroy, X., Tiu, A. (eds.) Proceedings of the 4th Conference on Certified Programs and Proofs (CPP 2015), pp. 59–66. ACM (2015)Google Scholar
  11. 11.
    Kühlwein, D., Blanchette, J.C., Kaliszyk, C., Urban, J.: MaSh: machine learning for Sledgehammer. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 35–50. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  12. 12.
    Otten, J.: Restricting backtracking in connection calculi. AI Commun. 23(2–3), 159–182 (2010)MATHMathSciNetGoogle Scholar
  13. 13.
    Otten, J., Bibel, W.: leanCoP: lean connection-based theorem proving. J. Symb. Comput. 36(1–2), 139–161 (2003)MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Schulz, S.: Learning Search Control Knowledge for Equational Deduction. DISKI, vol. 230. Infix Akademische Verlagsgesellschaft (2000)Google Scholar
  15. 15.
    Urban, J., Hoder, K., Voronkov, A.: Evaluation of automated theorem proving on the Mizar Mathematical Library. In: Fukuda, K., Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 155–166. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  16. 16.
    Urban, J., Vyskočil, J., Štěpánek, P.: MaLeCoP: Machine Learning Connection Prover. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 263–277. Springer, Heidelberg (2011) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of InnsbruckInnsbruckAustria
  2. 2.Czech Technical University in PraguePragueCzech Republic

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