Planning for distributed theorem proving: The teamwork approach

  • Jörg Denzinger
  • Martin Kronenburg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1137)


We present a new way to use planning in automated theorem proving by means of distribution. To overcome the problem that often subtasks of a problem cannot be detected a priori (which prevents the use of known planning and distribution techniques) we use the teamwork approach: A team of experts independently works on the problem with different heuristics. After a certain amount of time referees judge their results using the impact of the results on the behaviour of the experts. Then a supervisor combines the selected results to a new starting point. The supervisor also selects the experts that will work on the problem in the next round. This selection is a reactive planning task. We outline which information the supervisor can use to fulfill this task and how this information is processed to result in a plan or in revising a plan. Experimental results show that this planning approach for the assignment of experts to a team enables the system to solve many different examples in an acceptable time with the same start configuration and without any intervention by the user.


Theorem proving reactive planning distributed problem solving 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AD93]
    Avenhaus, J.; Denzinger, J.: Distributing equational theorem proving, Proc. 5th RTA, Montreal, LNCS 690, 1993, pp. 62–76.Google Scholar
  2. [BD88]
    Boddy, M.; Dean, T.: An Analysis of Time-Dependent Planning, Proc. 7. National Conf. on AI, Minneapolis, 1988, pp. 49–54.Google Scholar
  3. [BDP89]
    Bachmair, L.; Dershowitz, N.; Plaisted, D.A.: Completion without Failure, Coll. on the Resolution of Equations in Algebraic Structures, Austin (1987), Academic Press, 1989.Google Scholar
  4. [Be91]
    Beetz, M.: Decision-theoretic Transformational Planning, Internal report, Yale University, 1991.Google Scholar
  5. [Bu88]
    Bundy, A.: The use of explicit plans to guide inductive proofs, Proc. 9th CADE, 1988.Google Scholar
  6. [CL73]
    Chang, C.L.; Lee, R.C.: Symbolic Logic and Mechanical Theorem Proving, Academic Press, 1973.Google Scholar
  7. [De95]
    Denzinger, J.: Knowledge-Based Distributed Search Using Teamwork, Proc. ICMAS-95, San Francisco, AAAI-Press, 1995, pp. 81–88.Google Scholar
  8. [DF94]
    Denzinger, J.; Fuchs, M.: Goal oriented equational theorem proving using teamwork, Proc. KI-94, Saarbrücken, LNAI 861, 1994, pp. 343–354.Google Scholar
  9. [DL87]
    Durfee, E.H.; Lesser, V.R.: Using Partial Global Plans to Coordinate Distributed Problem Solvers, Proc. IJCAI-87, 1987, pp.875–883.Google Scholar
  10. [DS96]
    Denzinger, J.; Schulz, S.: Recording and Analyzing Knowledge-Based Distributed Deduction Processes, to appear in Journal of Symbolic Computation, 1996.Google Scholar
  11. [FHN81]
    Fikes, R.E.; Hart, P.E.; Nilsson, N.J.: Learning and executing generalized robot plans, in Webber, Nilsson (eds.) Readings in AI, 1981, pp.231–249.Google Scholar
  12. [HR87]
    Hsiang, J.; Rusinowitch, M.: On word problems in equational theories, Proc. 14th ICALP, Karlsruhe, LNCS 267, 1987, pp. 54–71.Google Scholar
  13. [Mc94]
    McCune, W.W.: OTTER 3.0 Reference manual and Guide, Tech. Rep. ANL-94/6, Argonne National Laboratory, 1994.Google Scholar
  14. [Mc90]
    Mc Dermott, D.: Planning reactive behaviour: A progress report, in J. Allen, J.Handler, A. Tate: Innovative Approaches to Planning, Scheduling and Control, Kaufmann, 1990, pp.450–458.Google Scholar
  15. [Ro82]
    Rosenschein, J.S.: Synchronization of Multi-Agent Plans, Proc. AAAI-82, 1982, pp.115–119.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jörg Denzinger
    • 1
  • Martin Kronenburg
    • 1
  1. 1.Department of Computer ScienceUniversity of KaiserslauternKaiserslautern

Personalised recommendations