Agent-Based HOL Reasoning

  • Alexander Steen
  • Max Wisniewski
  • Christoph Benzmüller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9725)

Abstract

In the Leo-III project, a new agent-based deduction system for classical higher-order logic is developed. Leo-III combines its predecessor’s concept of cooperating external specialist systems with a novel agent-based proof procedure. Key goals of the system’s development involve parallelism on various levels of the proof search, adaptability for different external specialists, and native support for reasoning in expressive non-classical logics.

Keywords

Higher-order logic Automated theorem proving Reasoning Non-classical logics 

References

  1. [BBK04]
    Benzmüller, C., Brown, C., Kohlhase, M.: Higher-order semantics and extensionality. J. Symbolic Logic 69(4), 1027–1088 (2004)MathSciNetCrossRefMATHGoogle Scholar
  2. [BDS13]
    Barendregt, H.P., Dekkers, W., Statman, R.: Lambda Calculus with Types. Perspectives in Logic. Cambridge University Press, Cambridge (2013)CrossRefMATHGoogle Scholar
  3. [Ben15a]
    Benzmüller, C.: Higher-order automated theorem provers. In: Delahaye, D., Woltzenlogel Paleo, B. (eds.) All About Proofs, Proof for All. Mathematical Logic and Foundations, pp. 171–214. College Publications, London (2015)Google Scholar
  4. [Ben15b]
    Benzmüller, C.: Invited talk: on a (quite) universal theorem proving approach and its application in metaphysics. In: De Nivelle, H. (ed.) TABLEAUX 2015. LNCS, vol. 9323, pp. 213–220. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  5. [BG94]
    Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. Logic Comput. 4(3), 217–247 (1994)MathSciNetCrossRefMATHGoogle Scholar
  6. [BJR15]
    Blanqui, F., Jouannaud, J.-P., Rubio, A.: The computability path ordering (2015). CoRR, abs/1506.03943Google Scholar
  7. [BM14]
    Benzmüller, C., Miller, D.: Automation of higher-order logic. In: Gabbay, D.M., Siekmann, J.H., Woods, J. (eds.) Handbook of the History of Logic. Computational Logic, vol. 9, pp. 215–254. Elsevier, North Holland (2014)Google Scholar
  8. [BPST15]
    Benzmüller, C., Paulson, L.C., Sultana, N., Theiß, F.: The higher-order prover LEO-II. J. Autom. Reasoning 55(4), 389–404 (2015)MathSciNetCrossRefMATHGoogle Scholar
  9. [Bro12]
    Brown, C.E.: Satallax: an automatic higher-order prover. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 111–117. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. [CEW11]
    Chalkiadakis, G., Elkind, E., Wooldridge, M.: Computational Aspects of Cooperative Game Theory. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers, San Rafael (2011)MATHGoogle Scholar
  11. [Chu40]
    Church, A.: A formulation of the simple theory of types. J. Symbolic Logic 5(2), 56–68 (1940)MathSciNetCrossRefMATHGoogle Scholar
  12. [Fre79]
    Frege, G.: Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Verlag von Louis Nebert, Halle (1879)Google Scholar
  13. [God31]
    Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. Monatshefte für Mathematik und Physik 38(1), 173–198 (1931)CrossRefMATHGoogle Scholar
  14. [Hen50]
    Henkin, L.: Completeness in the theory of types. J. Symbolic Logic 15(2), 81–91 (1950)MathSciNetCrossRefMATHGoogle Scholar
  15. [MP09]
    Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Appl. Logic 7(1), 41–57 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. [NPW02]
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL - A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)MATHGoogle Scholar
  17. [Sut09]
    Sutcliffe, G.: The TPTP problem library and associated infrastructure. J. Autom. Reasoning 43(4), 337–362 (2009)CrossRefMATHGoogle Scholar
  18. [WB16]
    Wisniewski, M., Benzmüller, C.: Is it reasonable to employ agents in theorem proving? In: van den Heerik, J., Filipe, J. (eds.) Proceedings of the 8th International Conference on Agents and Artificial Intelligence (ICAART), Rome, Italy, 2016, vol. 1, pp. 281–286. SCITEPRESS - Science and Technology Publications, Lda (2016)Google Scholar
  19. [Wei13]
    Weiss, G. (ed.): Multiagent Systems. MIT Press, Cambridge (2013)Google Scholar
  20. [Wis14]
    Wisniewski, M.: Agent-based Blackboard Architecture for a Higher-Order Theorem Prover. Master’s thesis, Freie Universität Berlin (2014)Google Scholar
  21. [WSB15]
    Wisniewski, M., Steen, A., Benzmüller, C.: LeoPARD — a generic platform for the implementation of higher-order reasoners. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS, vol. 9150, pp. 325–330. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  22. [WSKB16]
    Wisniewski, M., Steen, A., Kern, K., Benzmüller, C.: Effective normalization techniques for HOL. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS, vol. 9706, pp. 362–370. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-40229-1_25 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Alexander Steen
    • 1
  • Max Wisniewski
    • 1
  • Christoph Benzmüller
    • 1
    • 2
  1. 1.Institute of Computer ScienceFreie Universität BerlinBerlinGermany
  2. 2.CSLIStanford UniversityStanfordUSA

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