Erratum to : Learning-Assisted Automated Reasoning with Flyspeck (J Autom Reasoning, 10.1007/s10817-014-9303-3);Learning-assisted automated reasoning with Flyspeck

Journal of Automated Reasoning

Volumn 53, Issue 2, 2014, Pages 173-213

  Kaliszyk, Cezary ^a   Urban, Josef ^b  

^a UNIVERSITY OF INNSBRUCK   (Austria)

^b RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Artificial intelligence; Automated reasoning; Flyspeck; Formal mathematics; HOL light; Interactive theorem proving; Machine learning

Indexed keywords

ARTIFICIAL INTELLIGENCE; AUTOMATION; LEARNING SYSTEMS;

AUTOMATED REASONING; AUTOMATED THEOREM PROVER; DEPENDENCY INFORMATIONS; FLYSPECK; FORMAL MATHEMATICS; INTERACTIVE THEOREM PROVING; MATHEMATICAL KNOWLEDGE; SELECTION METHODS;

THEOREM PROVING;

EID: 84903814844     PISSN: 01687433     EISSN: 15730670     Source Type: Journal    
DOI: 10.1007/s10817-014-9315-z     Document Type: Erratum

References (89)

1. Adams, M.: Introducing HOL Zero- (extended abstract). In: Fukuda, K., van der Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS (LNCS), vol. 6327, pp 142-143. LNCS, Springer (2010)
2. Akbarpour, B., Paulson, L.C.: MetiTarski: an automatic theorem prover for real-valued special functions. J. Autom. Reason. 44(3), 175-205 (2010)
3. Alama, J., Brink, K., Mamane, L., Urban, J.: Large formal wikis: issues and solutions. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) Calculemus/MKM, vol. 6824, pp 133-148. LNCS, Springer (2011)
4. Alama, J., Heskes, T., Kühlwein, D., Tsivtsivadze, E., Urban, J.: Premise selection for mathematics by corpus analysis and kernel methods. J. Autom. Reason. 52(2), 191-213 (2014)
5. Alama, J., Kühlwein, D., Urban, J.: Automated and human proofs in general mathematics: an initial comparison. Bjrner, N., Voronkov, A. (eds.) Logic for Programming, Artificial Intelligence, and Reasoning - 18th International Conference, LPAR-18, Merida, Venezuela, March 11-15, 2012. Proceedings, vol. 7180, pp. 37-45. LNCS, Springer
6. Armando, A., Baumgartner, P., Dowek, G.: Automated Reasoning, 4th International Joint Conference, IJCAR 2008, Sydney, Australia, 12-15 August 2008. Proceedings, vol. 5195. LNCS, Springer (2008)
7. Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.): Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5-10, 2010. Proceedings, vol. 6167. LNCS, Springer (2010)
8. Beeson, M.: Automatic derivation of the irrationality of e. J. Symb. Comput. 32(4), 333-349 (2001) (Pubitemid 33098448)
9. Belinfante, J. G. F.: On computer-assisted proofs in ordinal number theory. J. Autom. Reason. 22(2), 341-378 (1999)
10. Benzmüller, C., Paulson, L.C., Theiss, F., Fietzke, A.: LEO-II - a cooperative automatic theorem prover for classical higher-order logic (system description). In: Armando, A., Baumgartner, P., Dowek, G., (eds.) Automated Reasoning, 4th International Joint Conference, IJCAR 2008, Sydney, Australia, August 12-15, 2008. Proceedings, vol. 5195, pp. 162-170. LNCS, Springer (2008)
11. Bjørner, N., Sofronie-Stokkermans, V. (eds.): Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, 31 July-5 August 2011. Proceedings, vol. 6803. LNCS, Springer (2011)
12. Bjørner, N., Voronkov, A. (eds.): Logic for Programming, Artificial Intelligence, and Reasoning - 18th International Conference, LPAR-18, Mérida, Venezuela, 11-15 March 2012. Proceedings, vol. 7180. LNCS, Springer (2012)
13. Blanchette, J. C.: Automatic Proofs and Refutations for Higher-Order Logic. PhD thesis, Fakultät für Informatik, Technische Universität München (2012). http://www21.in.tum.de/blanchet/phdthesis. pdf.
14. Blanchette, J.C., Böhme, S., Paulson, L.C.: Extending Sledgehammer with SMT solvers. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31 - August 5, 2011. Proceedings, vol. 6803, pp. 116-130. LNCS, Springer (2011)
15. Blanchette, J.C., Böhme, S., Popescu, A., Smallbone, N.: Encoding monomorphic and polymorphic types. In: Piterman, N., Smolka, S.A. (eds.) TACAS, Lecture Notes in Computer Science, vol. 7795, pp. 493-507. Springer (2013)
16. Blanchette, J.C., Bulwahn, L., Nipkow, T.: Automatic proof and disproof in Isabelle/HOL. In: Tinelli, C., Sofronie-Stokkermans, V. (eds.) FroCoS, vol. 6989, pp. 12-27. LNCS, Springer (2011)
17. Blanchette, J.C., Paskevich, A.: TFF1: the TPTP typed first-order form with rank-1 polymorphism. In: Bonacina, M.P. (ed.) CADE, Lecture Notes in Computer Science, vol. 7898, pp. 414-420. Springer (2013)
18. Blanchette, J.C., Popescu, A., Wand, D., Weidenbach, C.: More SPASS with Isabelle - superposition with hard sorts and configurable simplification. In: Beringer, L., Felty, A.P. (eds.) ITP, vol. 7406, pp. 345-360. LNCS, Springer (2012)
19. Böhme, S., Nipkow, T.: Sledgehammer: judgement day. In: Giesl, J., Hähnle, R. (eds.) IJCAR, vol. 6173, pp. 107-121. LNCS, Springer (2010)
20. Brown, C.E.: Satallax: an automatic higher-order prover. In: Gramlich, B., Miller, D., Sattler, U. (eds.) Automated Reasoning - 6th International Joint Conference, IJCAR 2012, Manchester, UK, June 26-29, 2012. Proceedings, vol. 7364, pp. 111-117. LNCS, Springer (2012)
21. Carlson, A., Cumby, C., Rosen, J., Roth, D.: The SNoW Learning Architecture, vol. 5 Technical Report UIUCDCS-R-99-2101, UIUC Computer Science Department (1999)
22. Church, A.: A formulation of the simple theory of types. J. Symb. Log. 5, 56-68 (1940)
23. Dahn, I.: Interpretation of a Mizar-like logic in first-order logic. In: Caferra, R., Salzer, G. (eds.) FTP (LNCS Selection), vol. 1761, pp. 137-151. LNCS, Springer (1998)
24. Dahn, I., Wernhard, C.: First order proof problems extracted from an article in the MIZAR Mathematical Library. In: Bonacina, M.P., Furbach, U. (eds.) International Workshop on First-Order Theorem Proving (FTP'97), RISC-Linz Report Series No. 97-50, pp. 58-62. Johannes Kepler Universität, Linz (Austria) (1997)
25. de Moura, L.M., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS, vol. 4963, pp. 337-340. LNCS, Springer (2008)
26. Filliâtre, J.-C., Marché, C.: The Why/Krakatoa/Caduceus platform for deductive program verification. In: Damm, W., Hermanns, H. (eds.) CAV, vol. 4590, pp. 173-177. LNCS, Springer (2007)
27. Furbach, U., Shankar, N. (eds.): Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20 2006. Proceedings, vol. 4130. LNCS, Springer (2006)
28. Van Gelder, A., Sutcliffe, G.: Extending the TPTP language to higher-order logic with automated parser generation. In: Furbach, U., Shankar, N. (eds.) Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006, Proceedings, vol. 4130, pp. 156-161. LNCS, Springer (2006)
29. Genesereth, M.R., Fikes, R. E.: Knowledge Interchange Format, Version 3.0 Reference Manual. Technical Report Logic-92-1, Computer Science Department, Stanford University (1992)
30. Gramlich, B., Miller, D., Sattler, U. (eds.): Automated Reasoning - 6th International Joint Conference, IJCAR 2012, Manchester, UK, 26-29 June 2012. Proceedings, vol. 7364. LNCS, Springer (2012)
31. Hähnle, R., Kerber, M., Weidenbach, C.: Common Syntax of the DFGSchwerpunktprogramm Deduction. Technical Report TR 10/96, Fakultät für Informatik, Universität Karlsruhe, Karlsruhe, Germany (1996)
32. Hales, T.C.: Introduction to the Flyspeck project. In: Coquand, T., Lombardi, H., Roy, M.-F. (eds.) Mathematics, Algorithms, Proofs, number 05021 in Dagstuhl Seminar Proceedings, pp. 1-11. Dagstuhl, Germany (2006). Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany
33. Hales, T. C. Mathematics in the age of the Turing machine. Lecture Notes in Logic (2012), to appear. http://www.math.pitt.edu/thales/papers/turing.pdf
34. Hales, T. C., Harrison, J., McLaughlin, S., Nipkow, T., Obua, S., Zumkeller, R.: A revision of the proof of the Kepler Conjecture. Discret. Comput. Geom. 44(1), 1-34 (2010)
35. Harrison, J.: HOL light: a tutorial introduction. In: Srivas, M.K., Camilleri, A.J. (eds.) FMCAD, vol. 1166, pp. 265-269. LNCS, Springer (1996) (Pubitemid 126149763)
36. Harrison, J.: A Mizar mode for HOL. In: von Wright, J., Grundy, J., Harrison, J. (eds.) TPHOLs, vol. 1125, pp. 203-220. LNCS, Springer (1996) (Pubitemid 126117973)
37. Harrison, J.: Optimizing proof search in model elimination. In: McRobbie, M., Slaney, J.K. (eds.) Proceedings of the 13th International Conference on Automated Deduction, vol. 1104, pp. 313-327. LNAI, Springer-Verlag (1996) (Pubitemid 126101559)
38. Hindley, R.: The principal type-scheme of an object in combinatory logic. Trans. Am. Math. Soc. 146, 29-60 (1969)
39. Hoder, K., Voronkov, A.: Sine qua non for large theory reasoning. In: Bjrner, N., Sofronie-Stokkermans, V. (eds.) Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31 - August 5, 2011. Proceedings, vol. 6803, pp. 299-314. LNCS, Springer (2011)
40. Hurd, J.: Integrating Gandalf and HOL. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs, vol. 1690, pp. 311-322. LNCS, Springer (1999)
41. Hurd, J.: An LCF-style interface between HOL and first-order logic. In: Voronkov, A. (ed.) CADE, Lecture Notes in Computer Science, vol. 2392, pp. 134-138. LNCS, Springer (2002)
42. Hurd, J.: First-order proof tactics in higher-order logic theorem provers. In: Archer, M., Di Vito, B., Muñoz, C. (eds.) Design and Application of Strategies/Tactics in Higher Order Logics (STRATA 2003), number NASA/CP-2003-212448 in NASA Technical, Reports, pp. 56-68, September (2003)
43. Kaliszyk, C.: Web interfaces for proof assistants. Electr. Notes Theor. Comput. Sci. 174(2), 49-61 (2007) (Pubitemid 46702850)
44. Kaliszyk, C., Krauss, A.: Scalable LCF-style proof translation. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) Proceedings of the 4th International Conference on Interactive Theorem Proving (ITP'13), vol. 7998, pp. 51-66. LNCS, Springer Verlag (2013)
45. Kaliszyk, C., Urban, J.: Initial experiments with external provers and premise selection on HOL Light corpora. In: Fontaine, P., Schmidt, R.A., Schulz, S. (eds.) PAAR-2012, EPiC Series, vol. 21, pp. 72-81. EasyChair (2013)
46. Kepler, J.: Strena seu de nive sexangula. Frankfurt: Gottfried. Tampach, 1611
47. Kovács, L., Voronkov, A.: First-order theorem proving and Vampire. In: Sharygina, N., Veith, H. (eds.) CAV, of Lecture Notes in Computer Science, vol. 8044, pp. 1-35. Springer (2013)
48. Kuehlwein, D., Urban, J.: Learning from multiple proofs: first experiments. In: Fontaine, P., Schmidt, R.A., Schulz, S. (eds.) PAAR-2012, volume 21 of EPiC Series, vol. 21, pp. 82-94. EasyChair (2013)
49. Kühlwein, D., van Laarhoven, T., Tsivtsivadze, E., Urban, J., Heskes, T.: Overview and evaluation of premise selection techniques for large theory mathematics. In: Gramlich, B., Miller, D., Sattler, U. (eds.) Automated Reasoning - 6th International Joint Conference, IJCAR 2012, Manchester, UK, June 26-29, 2012. Proceedings, vol. 7364, pp. 378-392. LNCS, Springer (2012)
50. Loveland, D. W.: Mechanical theorem proving by model elimination. J. ACM 15(2), 236-251 (1968)
51. Loveland, D. W.: Automated Theorem Proving: A Logical Basis. North-Holland, Amsterdam (1978)
52. McAllester, D. A.: Ontic: A Knowledge Representation System for Mathematics. MIT Press, Cambridge (1989)
53. McCune, W.: Prover9 and Mace4. http://www.cs.unm.edu/mccune/prover9/, (2005-2010)
54. McCune, W., Matlin, O.S.: Ivy: a preprocessor and proof checker for first-order logic. In: Kaufmann, M., Manolios, P., Strother Moore, J. (eds.) Computer-Aided Reasoning: ACL2 Case Studies, in Advances in Formal Methods, vol. 4, pp. 265-282. Kluwer Academic Publishers (2000)
55. McCune, W., Wos, L.: Otter: the CADE-13 competition incarnations. J. Autom. Reason. 18(2), 211-220 (1997) (Pubitemid 127715417)
56. Meier, A.: System description: tramp: transformation of machine-found proofs into nd-proofs at the assertion level. In: McAllester, D.A. (ed.) CADE, vol. 1831, pp. 460-464. LNCS, Springer (2000)
57. Meng, J., Paulson, L. C.: Translating higher-order clauses to first-order clauses. J. Autom. Reason. 40(1), 35-60 (2008)
58. Obua, S., Skalberg, S.: Importing hol into Isabelle/HOL. In: Furbach, U., Shankar, N. (eds.) Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006, vol. 4130, pp. 298-302. LNCS, Springer (2006) (Pubitemid 44532683)
59. Paulson, L. C.: A generic tableau prover and its integration with Isabelle. J. UCS 5(3), 73-87 (1999)
60. Paulson, L.C., Blanchette, J.: Three years of experience with Sledgehammer, a practical link between automated and interactive theorem provers. In: 8th IWIL (2010). Invited talk.
61. Paulson, L.C., Susanto, K.W.: Source-level proof reconstruction for interactive theorem proving. In: Schneider, K., Brandt, J. (eds.) TPHOLs, vol. 4732, pp. 232-245. LNCS, Springer (2007)
62. Pease, A., Sutcliffe, G.: First order reasoning on a large ontology. In: Sutclie, G., Urban, J., Schulz, S. (eds.) Proceedings of the CADE-21 Workshop on Empirically Successful Automated Reasoning in Large Theories, Bremen, Germany, 17th July 2007, CEUR Workshop, vol. 257. CEUR-WS.org (2007)
63. Pitts, A.: The HOL logic. In: Gordon, M.J.C., Melham, T.F. (eds.) Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press (1993)
64. Poincaré, H.: The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method. The Science Press, New York (1913)
65. Prevosto, V., Waldmann, U.: SPASS+T. In: Sutcliffe, G., Schmidt, R., Schulz, S. (eds.) ESCoR 2006, CEUR, vol. 192, pp. 18-33 (2006)
66. Quaife, A.: Automated Development of Fundamental Mathematical Theories. Kluwer Academic Publishers (1992)
67. Rudnicki, P., Trybulec, A.: On the integrity of a repository of formalized mathematics. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM, vol. 2594, pp. 162-174. LNCS, Springer (2003)
68. Schulz, S.: E - A Brainiac Theorem Prover. AI Commun. 15(2-3), 111-126 (2002) (Pubitemid 34838659)
69. Slind, K., Gordon, M.J.C., Boulton, R.J., Bundy, A.: System description: an interface between CLAM and HOL. In: Kirchner, C., Kirchner, H. (eds.) CADE, vol. 1421, pp. 134-138. LNCS, Springer (1998) (Pubitemid 128099542)
70. Sutcliffe, G., Benzmüller, C.: Automated reasoning in higher-order logic using the TPTP THF infrastructure. J. Formal. Reason. 3(1), 1-27 (2010)
71. Sutcliffe, G., Schulz, S., Claessen, K., Baumgartner, P.: The TPTP typed first-order form with arithmetic. In: Bjrner, N., Voronkov, A. (eds.) Logic for Programming, Artificial Intelligence, and Reasoning - 18th International Conference, LPAR-18, Merida, Venezuela, March 11-15, 2012. Proceedings, vol. 7180, pp. 406-419. LNCS, Springer (2012)
72. Sutcliffe, G., Schulz, S., Claessen, K., Van Gelder, A.: Using the TPTP language for writing derivations and finite interpretations. In: Furbach, U., Shankar, N. (eds.) Automated Reasoning, Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006. Proceedings, vol. 4130, pp. 67-81. LNCS, Springer (2006) (Pubitemid 44532663)
73. Sutcliffe, G., Urban, J., Schulz, S. (eds.): Proceedings of the CADE-21 Workshop on Empirically Successful Automated Reasoning in Large Theories, Bremen, Germany, 17th July 2007, CEUR Workshop Proceedings, vol. 257. CEUR-WS.org (2007)
74. Urban, J.: Translating Mizar for first order theorem provers. In: MKM, vol. 2594, pp. 203-215. LNCS, Springer (2003)
75. Urban, J.: MPTP - motivation, implementation, first experiments. J. Autom. Reason. 33(3-4), 319-339 (2004) (Pubitemid 40400718)
76. Urban, J.: MoMM - fast interreduction and retrieval in large libraries of formalized mathematics. Int. J. Artif. Intell. Tools 15(1), 109-130 (2006)
77. Urban, J.: MPTP 0.2: design, implementation, and initial experiments. J. Autom. Reason. 37(1-2), 21-43 (2006) (Pubitemid 46154516)
78. Urban, J.: An overview of methods 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)
79. Urban, J.: BliStr: The Blind Strategymaker. CoRR (2013). arXiv: 1301.2683
80. Urban, J., Rudnicki, P., Sutcliffe, G.: ATP and presentation service for Mizar formalizations. J. Autom. Reason. 50, 229-241 (2013)
81. Urban, J., Sutcliffe, G.: Automated reasoning and presentation support for formalizing mathematics in Mizar. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5-10, 2010. Proceedings, vol. 6167, pp. 132-146. LNCS, Springer (2010)
82. 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.) Automated Reasoning, 4th International Joint Conference, IJCAR 2008, Sydney, Australia, August 12-15, 2008. Proceedings, vol. 5195, pp. 441-456. LNCS, Springer (2008)
83. Urban, J., Vyskočil, J.: Theorem proving in large formal mathematics as an emerging AI field. In: Bonacina, M.P., Stickel, M.E. (eds.) Automated reasoning and mathematics: essays in memory of William McCune, vol. 7788, pp. 240-257. LNAI, Springer (2013)
84. Urban, J., Vyskočil, J., Štěpánek, P.: MaLeCoP: Machine learning connection prover. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX, vol. 6793, pp. 263-277. LNCS, Springer (2011)
85. Wall, L.: Programming Perl, 3rd edn. O'Reilly & Associates, Inc., Sebastopol (2000)
86. Weidenbach, C., Afshordel, B., Brahm, U., Cohrs, C., Engel, T., Keen, E., Theobalt, C., Topić, D.: System description: SPASS version 1.0.0. In: Automated Deduction - CADE-16, vol. 1632, pp. 378-382. LNCS, Springer Berlin Heidelberg (1999)
87. Weidenbach, C., Dimova, D., Fietzke, A., Kumar, R., Suda, M., Wischnewski, P.: SPASS Version 3.5. In: Schmidt, R.A. (ed.) CADE, vol. 5663, pp. 140-145. LNCS, Springer (2009)
88. Wiedijk, F.: Estimating the Cost of a Standard Library for a Mathematical Proof Checker. http://www.cs.ru.nl/freek/notes/mathstdlib2.pdf (2001)
89. Wiedijk, F.: A synthesis of the procedural and declarative styles of interactive theorem proving, Vol. 8 (2012)