Experiments with an Agent-Oriented Reasoning System

  • Christoph Benzmüller
  • Manfred Kerber
  • Mateja Jamnik
  • Volker Sorge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2174)


This paper discusses experiments with an agent oriented approach to automated and interactive reasoning. The approach combines ideas from two subfields of AI (theorem proving/proof planning and multi-agent systems) and makes use of state of the art distribution techniques to decentralise and spread its reasoning agents over the internet. It particularly supports cooperative proofs between reasoning systems which are strong in different application areas, e.g., higher-order and first-order theorem provers and computer algebra systems


Multiagent System Theorem Prover Computer Algebra System Natural Deduction Reasoning System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [ADF95]
    J. Avenhaus, J. Denzinger, and M. Fuchs. DISCOUNT:A system for distributed equational deduction. In Proc. of RTA-95, LNCS 914. Springer, 1995.Google Scholar
  2. [And72]
    P. Andrews. General models, descriptions and choice in type theory. Journal of Symbolic Logic, 37(2):385–394, 1972.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [AZ01]
    A. Armando and D. Zini. nterfacing computer algebra and deduction systems via the logic broker architecture. In [CAL01].Google Scholar
  4. [BCF+97]
    C. Benzmüller et al. Omega: Towards a mathematical assistant. In Proc. of CADE-14, LNAI 1249. Springer, 1997.Google Scholar
  5. [BJKS99]
    C. Benzmüller, M. Jamnik, M. Kerber, and V. Sorge. Agent Based Mathematical Reasoning. In CALCULEMUS-99, Systems for Integrated Computation and Deduction, volume 23 (3) of ENTCS. Elsevier, 1999.Google Scholar
  6. [BK98]
    C. Benzmüller and M. Kohlhase. LEO-a higher-order theorem prover. In Proc. of CADE-15, LNAI 1421. Springer, 1998.Google Scholar
  7. [Bon01]
    M. Bonacina. A taxonomy of parallel strategies for deduction. Annals of Mathematics and Artificial Intelligence, in press, 2001.Google Scholar
  8. [BS99]
    C. Benzmüller and V. Sorge. Critical Agents Supporting Interactive Theorem Proving. Proc. of EPIA-99, LNAI 1695, Springer, 1999.Google Scholar
  9. [BS01]
    C. Benzmüller and V. Sorge. OANTS-An open approach at combining Interactive and Automated Theorem Proving. In [CAL01].Google Scholar
  10. [CAL01]
    CALCULEMUS-2000, Systems for Integrated Computation and Deduction. AK Peters, 2001.Google Scholar
  11. [CS00]
    L. Cheikhrouhou and V. Sorge. PDS A Three-Dimensional Data Structure for Proof Plans. In Proc. of ACIDCA’2000, 2000.Google Scholar
  12. [DD98]
    I. Dahn and J. Denzinger. Cooperating theorem provers. In Automated Deduction-A Basis for Applications, volume II. Kluwer, 1998.Google Scholar
  13. [DF99]
    J. Denzinger and D. Fuchs. Cooperation of Heterogeneous Provers. In Proc. of IJCAI-99, 1999.Google Scholar
  14. [DK96]
    J. Denzinger and M. Kronenburg. Planning for distributed theorem proving: The teamwork approach. In Proc. of KI-96, LNAI 1137. Springer, 1996.Google Scholar
  15. [FHJ+99]
    A. Franke, S. Hess, Ch. Jung, M. Kohlhase, and V. Sorge. Agent-Oriented Integration of Distributed Mathematical Services. Journal of Universal Computer Science, 5(3):156–187, 1999.zbMATHGoogle Scholar
  16. [FI98]
    M. Fisher and A. Ireland. Multi-agent proof-planning. CADE-15Workshop “Using AI methods in Deduction”, 1998.Google Scholar
  17. [Fie01]
    A. Fiedler. P.rex: An interactive proof explainer. In R. Goré, A. Leitsch, and T. Nipkow (eds), Automated Reasoning-Proceedings of the First International Joint Conference, IJCAR, LNAI 2083. Springer, 2001.Google Scholar
  18. [Fis97]
    M. Fisher. An Open Approach to Concurrent Theorem Proving. In Parallel Processing for Artificial Intelligence, volume 3. Elsevier, 1997.Google Scholar
  19. [FW95]
    M. Fisher and M. Wooldridge. A Logical Approach to the Representation of Societies of Agents. In Artificial Societies. UCL Press, 1995.Google Scholar
  20. [IB95]
    A. Ireland and A. Bundy. Productive use of failure in inductive proof. Special Issue of the Journal of Automated Reasoning, 16(1-2):79–111, 1995.CrossRefMathSciNetGoogle Scholar
  21. [Mei00]
    A. Meier. Tramp-transformation of machine-found proofs into ND-proofs at the assertion level. In Proc. of CADE-17, LNAI 1831. Springer, 2000.Google Scholar
  22. [Mül97]
    J. Müller. A Cooperation Model for Autonomous Agents. In Proc. of the ECAI’96 Workshop Intelligent Agents III, LNAI 1193. Springer, 1997.Google Scholar
  23. [NFAR82]
    H. Nii, E. Feigenbaum, J. Anton, and A. Rockmore. Signal-to-symbol transformation: HASP/SIAP case study. AIMagazine, 3(2):23–35, 1982.Google Scholar
  24. [Ric89]
    J. Rice. The ELINT Application on Poligon: The Architecture and Performance of a Concurrent Blackboard System. In Proc. of IJCAI-89. Morgan Kaufmann, 1989.Google Scholar
  25. [SHB+99]
    J. Siekmann et al. Loui: Lovely Omega user interface. Formal Aspects of Computing, 11(3):326–342, 1999.CrossRefGoogle Scholar
  26. ed][Wei99]
    G. Weiss, editor. Multiagent systems: a modern approach to distributed artificial intelligence. MIT Press, 1999.Google Scholar
  27. [Wol98]
    A. Wolf. P-SETHEO: Strategy Parallelism in Automated Theorem Proving. In Proc. of TABLEAUX-98, LNAI 1397. Springer, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Christoph Benzmüller
    • 1
  • Manfred Kerber
    • 2
  • Mateja Jamnik
  • Volker Sorge
    • 1
  1. 1.Fachbereich InformatikUniversität des SaarlandesSaarbrückenGermany
  2. 2.School of Computer ScienceThe University of BirminghamEnglandUK

Personalised recommendations