Overview and evaluation of premise selection techniques for large theory mathematics

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7364 LNAI, Issue , 2012, Pages 378-392

  Kühlwein, Daniel ^a   Van Laarhoven, Twan ^a   Tsivtsivadze, Evgeni ^a   Urban, Josef ^a   Heskes, Tom ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATED REASONING; EVALUATION METRICS; SELECTION TECHNIQUES;

ARTIFICIAL INTELLIGENCE;

MATHEMATICAL TECHNIQUES;

EID: 84863617445     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-31365-3_30     Document Type: Conference Paper

References (40)

1. Alama, J., Heskes, T., Kühlwein, D., Tsivtsivadze, E., Urban, J.: Premise Selection for Mathematics by Corpus Analysis and Kernel Methods. CoRR abs/1108.3446 (2011)
2. Alama, J., Kühlwein, D., Urban, J.: Automated and Human Proofs in General Mathematics: An Initial Comparison. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 37-45. Springer, Heidelberg (2012)
3. Bem, J.: The Zermelo proof checker, http://zermelo.org/
4. Bingham, E., Mannila, H.: Random projection in dimensionality reduction: applications to image and text data. In: KDD, pp. 245-250 (2001)
5. Blanchette, J.C., Bulwahn, L., Nipkow, T.: Automatic Proof and Disproof in Isabelle/HOL. In: Tinelli, C., Sofronie-Stokkermans, V. (eds.) FroCos 2011. LNCS, vol. 6989, pp. 12-27. Springer, Heidelberg (2011)
6. Carlson, A., Cumby, C., Rosen, J., Roth, D.: The SNoW Learning Architecture. Tech. Rep. UIUCDCS-R-99-2101, UIUC Computer Science Department (May 1999), http://cogcomp.cs.illinois.edu/papers/CCRR99.pdf
7. Chu, W., Park, S.T.: Personalized recommendation on dynamic content using predictive bilinear models. In: Quemada, J., León, G., Maarek, Y.S., Nejdl, W. (eds.) WWW, pp. 691-700. ACM (2009)
8. Cramer, M., Fisseni, B., Koepke, P., Kühlwein, D., Schröder, B., Veldman, J.: The Naproche Project Controlled Natural Language Proof Checking of Mathematical Texts. In: Fuchs, N.E. (ed.) CNL 2009. LNCS, vol. 5972, pp. 170-186. Springer, Heidelberg (2010)
9. Deerwester, S.C., Dumais, S.T., Landauer, T.K., Furnas, G.W., Harshman, R.A.: Indexing by Latent Semantic Analysis. JASIS 41(6), 391-407 (1990)
10. Denzinger, J., Fuchs, M., Goller, C., Schulz, S.: Learning from Previous Proof Experience. Technical Report AR99-4, Institut für Informatik, Technische Universität München (1999)
11. Gonthier, G.: Advances in the Formalization of the Odd Order Theorem. In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, p. 2. Springer, Heidelberg (2011)
12. Hales, T.C.: Mathematics in the age of the Turing machine. Lecture Notes in Logic (to appear, 2012), http://www.math.pitt.edu/~thales/papers/turing.pdf
13. Hales, T.C., Harrison, J., McLaughlin, S., Nipkow, T., Obua, S., Zumkeller, R.: A revision of the proof of the Kepler Conjecture. Discrete & Computational Geometry 44(1), 1-34 (2010)
14. Hoder, K., Voronkov, A.: Sine Qua Non for Large Theory Reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 299-314. Springer, Heidelberg (2011)
15. Klein, G., Andronick, J., Elphinstone, K., Heiser, G., Cock, D., Derrin, P., Elkaduwe, D., Engelhardt, K., Kolanski, R., Norrish, M., Sewell, T., Tuch, H., Winwood, S.: seL4: formal verification of an operating-system kernel. Commun. ACM 53(6), 107-115 (2010)
16. McCune, W.: Prover9 and Mace4 (2005-2010), http://www.cs.unm.edu/~mccune/ prover9/
17. Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Applied Logic 7(1), 41-57 (2009)
18. de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337-340. Springer, Heidelberg (2008)
19. Otten, J., Bibel, W.: leanCoP: lean connection-based theorem proving. J. Symb. Comput. 36(1-2), 139-161 (2003)
20. Polikar, R.: Ensemble based systems in decision making. IEEE Circuits and Systems Magazine 6(3), 21-45 (2006)
21. Pudlak, P.: Semantic Selection of Premisses for Automated Theorem Proving. In: Sutcliffe et al. [31]
22. Reichelt, S.: The HLM proof assistant, http://hlm.sourceforge.net/
23. Riazanov, A., Voronkov, A.: The design and implementation of VAMPIRE. AI Commun. 15(2-3), 91-110 (2002)
24. Roederer, A., Puzis, Y., Sutcliffe, G.: Divvy: An ATP Meta-system Based on Axiom Relevance Ordering. In: Schmidt [25], pp. 157-162
25. Schmidt, R.A. (ed.): CADE-22. LNCS, vol. 5663. Springer, Heidelberg (2009)
26. Schulz, S.: Learning search control knowledge for equational deduction. DISKI, vol. 230. Infix Akademische Verlagsgesellschaft (2000)
27. Schulz, S.: E - A Brainiac Theorem Prover. AI Commun. 15(2-3), 111-126 (2002)
28. Sculley, D.: Rank aggregation for similar items. In: SDM. SIAM (2007)
29. Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, New York (2004)
30. Sutcliffe, G., Puzis, Y.: SRASS - A Semantic Relevance Axiom Selection System. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 295-310. Springer, Heidelberg (2007) (Pubitemid 47545117)
31. Sutcliffe, G., Urban, J., Schulz, S. (eds.): Proceedings of the CADE-21Workshop on Empirically Successful Automated Reasoning in Large Theories, Bremen, Germany, July 17. CEUR Workshop Proceedings, vol. 257. CEUR-WS.org (2007)
32. Urban, J.: MizarMode-an integrated proof assistance tool for the Mizar way of formalizing mathematics. Journal of Applied Logic 4(4), 414-427 (2006)
33. Urban, J.: MaLARea: a metasystem for automated reasoning in large theories. In: Sutcliffe et al. [31]
34. Urban, J.: An Overview ofMethods for Large-Theory Automated Theorem Proving (Invited Paper). In: Höfner, P., McIver, A., Struth, G. (eds.) ATE Workshop. CEUR Workshop Proceedings, vol. 760, pp. 3-8. CEUR-WS.org (2011)
35. Urban, J., Hoder, K., Voronkov, A.: Evaluation of Automated Theorem Proving on the Mizar Mathematical Library. In: Fukuda, K., van der Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 155-166. Springer, Heidelberg (2010)
36. Urban, J., Rudnicki, P., Sutcliffe, G.: ATP and presentation service for Mizar formalizations. CoRR abs/1109.0616 (2011)
37. Urban, J., Sutcliffe, G., Pudlák, P., Vyskočil, J.: MaLARea SG1 - Machine Learner for Automated Reasoning with Semantic Guidance. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 441-456. Springer, Heidelberg (2008)
38. 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)
39. Voevodsky, V.: Univalent foundations project (2010) (manuscript), http://www.math.ias.edu/~vladimir/Site3/Univalent-Foundations.html
40. Weidenbach, C., Dimova, D., Fietzke, A., Kumar, R., Suda, M., Wischnewski, P.: SPASS Version 3.5. In: Schmidt [25], pp. 140-145