MaLARea: a Metasystem for Automated Reasoning in Large Theories. MaLARea (a Machine Learner for Automated Reasoning) is a simple metasystem iteratively combining deductive Automated Reasoning tools (now the E and the SPASS ATP systems) with a machine learning component (now the SNoW system used in the naive Bayesian learning mode). Its intended use is in large theories, i.e. on a large number of problems which in a consistent fashion use many axioms, lemmas, theorems, definitions and symbols. The system works in cycles of theorem proving followed by machine learning from successful proofs, using the learned information to prune the set of available axioms for the next theorem proving cycle. Although the metasystem is quite simple (ca. 1000 lines of Perl code), its design already now poses quite interesting questions about the nature of thinking, in particular, about how (and if and when) to combine learning from previous experience to attack difficult unsolved problems. The first version of MaLARea has been tested on the more difficult (chainy) division of the MPTP Challenge solving 142 problems out of 252, in comparison to E’s 89 and SPASS ’ 81 solved problems. It also outperforms the SRASS metasystem, which also uses E and SPASS as components, and solves 126 problems.

References in zbMATH (referenced in 27 articles )

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  1. Blanchette, Jasmin Christian; Greenaway, David; Kaliszyk, Cezary; Kühlwein, Daniel; Urban, Josef: A learning-based fact selector for Isabelle/HOL (2016)
  2. Jan Jakubuv, Josef Urban: BliStrTune: Hierarchical Invention of Theorem Proving Strategies (2016) arXiv
  3. Furbach, Ulrich; Pelzer, Björn; Schon, Claudia: Automated reasoning in the wild (2015)
  4. Kaliszyk, Cezary; Urban, Josef: HOL(y)Hammer: online ATP service for HOL Light (2015)
  5. Kaliszyk, Cezary; Urban, Josef: MizAR 40 for Mizar 40 (2015)
  6. Kaliszyk, Cezary; Urban, Josef: Learning-assisted theorem proving with millions of lemmas (2015)
  7. Alama, Jesse; Heskes, Tom; Kühlwein, Daniel; Tsivtsivadze, Evgeni; Urban, Josef: Premise selection for mathematics by corpus analysis and kernel methods (2014)
  8. Bridge, James P.; Holden, Sean B.; Paulson, Lawrence C.: Machine learning for first-order theorem proving (2014)
  9. Kaliszyk, Cezary; Urban, Josef: Learning-assisted automated reasoning with $\mathsfFlyspeck$ (2014)
  10. Heras, Jónathan; Komendantskaya, Ekaterina; Johansson, Moa; Maclean, Ewen: Proof-pattern recognition and lemma discovery in ACL2 (2013)
  11. Kaliszyk, Cezary; Urban, Josef: Automated reasoning service for HOL light (2013)
  12. Kühlwein, Daniel; Schulz, Stephan; Urban, Josef: E-MaLeS 1.1 (2013)
  13. Urban, Josef; Rudnicki, Piotr; Sutcliffe, Geoff: ATP and presentation service for Mizar formalizations (2013)
  14. Urban, Josef; Vyskočil, Jiří: Theorem proving in large formal mathematics as an emerging AI field (2013)
  15. Alama, Jesse; Kühlwein, Daniel; Urban, Josef: Automated and human proofs in general mathematics: an initial comparison (2012)
  16. Kühlwein, Daniel; van Laarhoven, Twan; Tsivtsivadze, Evgeni; Urban, Josef; Heskes, Tom: Overview and evaluation of premise selection techniques for large theory mathematics (2012)
  17. Urban, Josef; Vyskočil, Jiří; Štěpánek, Petr: MaLeCoP. Machine learning connection prover (2011)
  18. Cramer, Marcos; Koepke, Peter; Kühlwein, Daniel; Schröder, Bernhard: Premise selection in the Naproche system (2010)
  19. Pease, Adam; Sutcliffe, Geoff; Siegel, Nick; Trac, Steven: Large theory reasoning with SUMO at CASC (2010)
  20. Urban, Josef; Hoder, Krystof; Voronkov, Andrei: Evaluation of automated theorem proving on the Mizar mathematical library (2010)

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