Abstract
One possible way to deal with large theories is to have a good selection method for relevant axioms. This is confirmed by the fact that the largest available first-order knowledge base (the Open CYC) contains over 3 million axioms, while answering queries to it usually requires not more than a few dozen axioms. A method for axiom selection has been proposed by the first author in the Sumo INference Engine (SInE) system. SInE has won the large theory division of CASC in 2008. The method turned out to be so successful that the next two years it was used by the winner as well as by several other competing systems. This paper contains the presentation of the method and describes experiments with it in the theorem prover Vampire.
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References
Roederer, A., Puzis, Y., Sutcliffe, G.: divvy: An ATP meta-system based on axiom relevance ordering. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 157–162. Springer, Heidelberg (2009)
Armando, A., Baumgartner, P., Dowek, G. (eds.): IJCAR 2008. LNCS (LNAI), vol. 5195. Springer, Heidelberg (2008)
Hoder, K., Kovács, L., Voronkov, A.: Interpolation and symbol elimination in vampire. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 188–195. Springer, Heidelberg (2010)
Lenat, D.B.: CYC: A large-scale investment in knowledge infrastructure. Communications of the ACM 38(11), 33–38 (1995)
Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Applied Logic 7(1), 41–57 (2009)
Niles, I., Pease, A.: Towards a standard upper ontology. In: FOIS, pp. 2–9 (2001)
Plaisted, D.A., Yahya, A.H.: A relevance restriction strategy for automated deduction. Artif. Intell. 144(1-2), 59–93 (2003)
Pudlak, P.: Semantic selection of premisses for automated theorem proving. In: Sutcliffe, G., Urban, J., Schulz, S. (eds.) ESARLT. CEUR Workshop Proceedings, vol. 257, pp. 27–44. (2007) CEUR-WS.org
Rudnicki, P. (ed.): An overview of the mizar project, pp. 311–332. University of Technology, Bastad (1992)
Sutcliffe, G.: CASC-J4 the 4th IJCAR ATP system competition. In: Armando (ed.) [2], pp. 457–458
Sutcliffe, G.: The tptp problem library and associated infrastructure. J. Autom. Reasoning 43(4), 337–362 (2009)
Sutcliffe, G.: The cade-22 automated theorem proving system competition - casc-22. AI Commun. 23(1), 47–59 (2010)
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)
Urban, J.: Mptp 0.2: Design, implementation, and initial experiments. J. Autom. Reasoning 37(1-2), 21–43 (2006)
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)
Urban, J., Sutcliffe, G., Pudlák, P., Vyskocil, J.: Malarea sg1- machine learner for automated reasoning with semantic guidance. In: Armando (ed.) [2], pp. 441–456.
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Hoder, K., Voronkov, A. (2011). Sine Qua Non for Large Theory Reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) Automated Deduction – CADE-23. CADE 2011. Lecture Notes in Computer Science(), vol 6803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22438-6_23
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DOI: https://doi.org/10.1007/978-3-642-22438-6_23
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