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Octopus: combining learning and parallel search. (English) Zbl 1102.68647
Summary: This paper presents Octopus, an automated theorem-proving system that combines learning and parallel search. The learning technique involves proving a simpler version of a given theorem and then using what it has learned to prove the given theorem. As of January 2004 Octopus had successfully proved 43 of the 1.0-rated theorems of the TPTP Problem Library.

MSC:
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
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[1] Newborn, M.: Automated Theorem Proving: Theory and Practice, Springer-Verlag, New York, 2001. · Zbl 0963.68176
[2] Sutcliffe, G. and Suttner, C. B.: The TPTP problem library, J. Automated Reasoning 21(2) (1998), 177-203. · Zbl 0910.68197 · doi:10.1023/A:1005806324129
[3] http://www.cs.miami.edu/\(\sim\)tptp/
[4] http://www.cs.miami.edu/\(\sim\)tptp/CASC/
[5] Newborn, M.: Proofs of twenty-four 1.0-rated theorems in the TPTP problem library, TR SOCS-03.6, School of Computer Science, McGill University, Montreal, 2003.
[6] Newborn, M. and Wang, Z.: Proofs of nineteen more 1.0 rated theorems in the TPTP problem library, TR SOCS-04.1, School of Computer Science, McGill University, Montreal, 2004.
[7] Plaisted, D. A.: Theorem proving with abstraction, Artificial Intelligence 16(1) (1981), 47-108. · Zbl 0454.68113 · doi:10.1016/0004-3702(81)90015-1
[8] Kling, R. E.: A paradigm for reasoning by analogy, Artificial Intelligence 2(2) (1971), 147-178. · Zbl 0227.68041 · doi:10.1016/0004-3702(71)90008-7
[9] Greiner, R.: Learning and understanding by analogies, Artificial Intelligence 35(1) (1988), 81-125. · Zbl 0646.68095 · doi:10.1016/0004-3702(88)90032-X
[10] Brock, B., Cooper, S. and Pierce, W.: Analogical reasoning and proof discovery, in E. Lusk and R. A. Overbeek (eds.), Proc. 9th Conf. on Automated Deduction, Argonne, IL, LNCS 310, Springer-Verlag, 1988, pp. 454-468. · Zbl 0666.68096
[11] Carbonell, J. G. and Veloso, M.: Integrating derivational analogy into a general problem solving architecture, in J. Kolodner (ed.), Proc. 1988 DARPA Workshop on Case-Based Reasoning, Clearwater Beach, 1988.
[12] Kolbe, T. and Brauburger, J.: Plagiator ? a learning prover, in W. McCune (ed.), Proc. 14th Int. Conf. on Automated Deduction, LNCS 1249, Springer-Verlag, 1997, pp. 256-259.
[13] Kolbe, T. and Walther, C.: Reusing proofs, in A. G. Cohn (ed.), Proc. 11th European Conf. on Artificial Intelligence, Amsterdam, Wiley, 1994, pp. 80-84.
[14] Melis, E.: A model of analogy-driven proof-plan construction, in C. S. Mellish (ed.), Proc. 14th Int. Joint Conf. on Artificial Intelligence, Morgan Kaufmann, 1995, pp. 182-189.
[15] Draeger, J.: Acquisition of useful lemma knowledge in automated reasoning, in F. Giunchiglia (ed.), Proc. 8th Int. Conf. on Artificial Intelligence: Methodology, Systems, and Applications, LNCS 1480, Springer-Verlag, 1998, pp. 230-239.
[16] Fuchs, M.: Experiments in the heuristic use of past proof experience, in M. A. McRobbie and J. K. Slaney (eds.), Proc. 13th Conf. on Automated Deduction, LNAI 1104, Springer-Verlag, 1996, pp. 523-537.
[17] Denzinger, J. and Schulz, S.: Learning domain knowledge to improve theorem proving, in M. A. McRobbie and J. K. Slaney (eds.), Proc. 13th Conf. on Automated Deduction, LNAI 1104, Springer-Verlag, 1996, pp. 62-76.
[18] Denzinger, J., Fuchs, M., Goller, C. and Schulz, S.: Learning from previous proof experience: A survey, Report AR-99-4, Fakultät für Informatik der Technischen Universität München, 1999.
[19] Bonacina, M. P.: A taxonomy of parallel strategies for deduction, Ann. Math. Artificial Intelligence 29(1-4) (2000), 223-257. · Zbl 1001.68124 · doi:10.1023/A:1018932114059
[20] Jindal, A., Overbeek, R. and Kabat, W.: Exploitation of parallel processing for implementing high-performance deduction systems, J. Automated Reasoning 8(1) (1992), 23-38. · doi:10.1007/BF00263447
[21] Lusk, E. L. and McCune, W. W.: Experiments with ROO: A parallel automated deduction system, in B. Fronhofer and G. Wrightson (eds.), Parallelization in Inference Systems, LNAI 590, Springer-Verlag, 1990, pp. 139-162.
[22] Lusk, E., McCune, W. and Slaney, J.: ROO ? a parallel theorem prover, ANL/MCS-TM-149, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1991.
[23] Lusk, E. L., McCune, W. W. and Slaney, J. K.: ROO: A parallel theorem prover, in D. Kapur (ed.), Proc. 11th Int. Conf. on Automated Deduction, Saratoga Springs, June 15-18, LNAI 607, Springer-Verlag, 1992, pp. 731-734.
[24] Bonacina, M. P. and Hsiang, J.: Distributed deduction by clause-diffusion: Distributed contraction and the Aquarius prover, J. Symbolic Computation 19(3) (1995), 245-267. · Zbl 0836.68105 · doi:10.1006/jsco.1995.1014
[25] Bonacina, M. P.: Combination of distributed search and multi-search in Peers-mcd.d, in R. Gore, A. Leitsch and T. Nipkow (eds.), Proc. 1st Int. Joint Conf. on Automated Reasoning, Siena, Italy, June 18-23, LNAI 2083, Springer-Verlag, 2001, pp. 448-452. · Zbl 0988.68611
[26] Bonacina, M. P.: The clause-diffusion theorem prover Peers-mcd (system description), in W. McCune (ed.), Proc. 14th Int. Conf. on Automated Deduction, Townsville, Australia, July 13-17, LNCS 1249, Springer-Verlag, 1997, pp. 53-56.
[27] McCune, W.: Otter 3.3 reference manual, Technical Memorandum No. 263, Mathematics and Computer Science Division, Argonne National Laboratory, 2003 (http://www-unix.mcs.anl.gov/AR/otter/otter33.pdf).
[28] McCune, W.: 33 basic test problems: A practical evaluation of some paramodulation strategies, in R. Veroff (ed.), Automated Reasoning and Its Applications: Essays in Honor of Larry Wos, MIT Press, 1997.
[29] Letz, R., Bayerl, S., Schumann, J. and Bibil, W.: SETHEO ? a high-performance theorem prover, J. Symbolic Computation 15(5/6) (1992), 183-212. · Zbl 0759.68080
[30] Fuchs, M. and Wolf, A.: System description ? Cooperation in model elimination: CPTHEO, in C. Kirchner and H. Kirchner (eds.), Proc. 15th Int. Conf. on Automated Deduction, LNCS 1421, Springer-Verlag, 1998, pp. 42-46.
[31] Schumann, J. and Letz, R.: PARTHEO: A high performance parallel theorem prover, in M. E. Stickel (ed.), Proc. 10th Int. Conf. on Automated Deduction, LNAI 449, Springer-Verlag, 1990, pp. 40-56. · Zbl 0708.68076
[32] Bose, S., Clarke, E. M., Long, D. E. and Michaylov, S.: PARTHENON: A parallel theorem prover for non-Horn clauses, J. Automated Reasoning 8(2) (1992), 153-181. · Zbl 0759.68079 · doi:10.1007/BF00244281
[33] Astrachan, O.: METEOR: Exploring model elimination theorem proving, J. Automated Reasoning 13(3) (1994), 283-296. · Zbl 00724132 · doi:10.1007/BF00881946
[34] Astrachan, O. L. and Loveland, D. W.: METEORs: High performance theorem provers using model elimination, in R. S. Boyer (ed.), Automated Reasoning: Essays in Honor of Woody Bledsoe, Kluwer, 1991, pp. 31-60.
[35] MacIntosh, D. J., Conry, S. E. and Meyer, R. A.: Distributed automated reasoning: Issues in coordination, cooperation and performance, IEEE Trans. Systems, Man, Cybernet. 21(6) (1991), 1307-1316. · doi:10.1109/21.135677
[36] Denzinger, J., Kronenburg, M. and Schulz, S.: DISCOUNT ? a distributed and learning equational prover, J. Automated Reasoning 18(2) (1997), 189-198. · Zbl 05468571 · doi:10.1023/A:1005879229581
[37] Denzinger, J. and Fuchs, D.: Cooperation of heterogeneous provers, in T. Dean (ed.), Proc. of the 16th Int. Joint Conf. on Artificial Intelligence, Stockholm, Sweden, July 31?August 6, Morgan Kaufmann, 1999, pp. 10-15.
[38] Weidenbach, C.: Spass: Version 0.49, J. Automated Reasoning 18(2) (1997), 247-252. · Zbl 05468578 · doi:10.1023/A:1005812220011
[39] Suttner, C. B.: SPTHEO ? A parallel theorem prover, J. Automated Reasoning 18(2) (1997), 253-258. · Zbl 05468579 · doi:10.1023/A:1005868304990
[40] Suttner, C. B.: SPS-Parallelism+SETHEO=SPTHEO, J. Automated Reasoning 22(4) (1999), 397-431. · Zbl 0929.68111 · doi:10.1023/A:1006127022180
[41] Wolf, A.: p-SETHEO: Strategy parallelism in automated theorem proving, in H. de Swert (ed.), Proc. Int. Conf. TABLEAUX?98: Analytic Tableaux and Related Methods, LNAI 397, Springer-Verlag, 1998, pp. 320-324.
[42] Schumann, J.: SiCoTHEO ? Simple competitive parallel theorem provers based on SETHEO, in J. Geller, H. Kitano and C. B. Suttner (eds.), Parallel Processing for Artificial Intelligence 3, Elsevier, 1997, pp. 231-245.
[43] Sutcliffe, G. and Seyfang, D.: Smart selective competition parallelism ATP, in A. Kumar and I. Russell (eds.), Proc. 12th Florida Artificial Intelligence Research Symposium, Orlando, FL, May 3-5, American Association for Artificial Intelligence Press, 1999, pp. 341-345.
[44] De Nivelle, H.: Bliksem 1.00, in C. Kirchner and H. Kirchner (eds.), Proc. 15th Int. Conf. on Automated Deduction, Lindau, Germany, July 5-10, LNCS 1421, Springer-Verlag, 1998, p. 9.
[45] Tammet, T.: Gandalf, J. Automated Reasoning 18(2) (1997), 247-252. · Zbl 05468572 · doi:10.1023/A:1005887414560
[46] McCune, W.: Otter 3.3 Reference Manual, Technical Memorandum No. 249, Mathematics and Computer Science Division, Argonne National Laboratory, 2001 (http://www-unix.mcs.anl.gov/AR/mace2/mace2.pdf).
[47] http://www.cs.miami.edu/\(\sim\)tptp/CASC/16/
[48] Newborn, M.: The Great Theorem Prover, Newborn Software, 1989.
[49] http://www.cs.miami.edu/\(\sim\)tptp/CASC/19/
[50] Geist, A., Beguelin, A., Dongarra, J., Jiang, W., Manchek, R. and Sunderam, V.: PVM: Parallel Virtual Machine, MIT Press, 1994. · Zbl 0849.68032
[51] Draeger, J.: Anwendung des Theorembeweisers SETHEO auf angeordnete Körper, FKI-186-93, Technische Universität München, Munich, 1993.
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