Optimal strategies — Learning from examples — Boolean equations

  • Christian Posthoff
  • Michael Schlosser
2 Inductive Inference for Artificial Intelligence 2.1 Theoretical Approaches
Part of the Lecture Notes in Computer Science book series (LNCS, volume 961)


The paper covers a wide range of knowledge acquisition, knowledge engineering and Machine Learning. The main idea is to unify a lot of AI problems using set-theoretic concepts and logical functions.

Many concepts of knowledge-based problem-solving are incorporated into one system which has been based on set-theoretical concepts. This results in a consisting methodology and in a comprehensive set of tools applicable in many fields. The transition between fuzzy and non-fuzzy parts of the problem domain can be realized very flexible supplying a high smartness and a high performance of the constructed model.

Part A of the paper shows the basis for different Machine Learning methods using logical equations. Part B gives a way how to use optimal strategies in order to obtain complete knowledge. A few examples illustrate the method.


Logical Equation Disjunctive Normal Form Binary Attribute Fuzzy Equivalence Relation Boolean Equation 
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.


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  1. [AB92]
    M. Anthony and N. Biggs. Computational Learning Theory. An Introduction. Cambridge University Press, Cambridge, 1992.Google Scholar
  2. [BC80]
    D. F. Beal and M. R. B. Clarke. The Construction of Economical and Correct Algorithms for King and Pawn against King. In M. R. B. Clarke, editor, Advances in Computer Chess 2, pages 1–30, Edinburgh, Scotland, 1980. Edinburgh Univ. Press.Google Scholar
  3. [BP81]
    D. Bochmann and Chr. Posthoff. Binäre dynamische Systeme. Akademie-Verlag, Berlin, 1981.Google Scholar
  4. [BS91]
    D. Bochmann and B. Steinbach. Logikentwurf mit XBOOLE, Algorithmen und Programme. Verlag Technik GmbH, Berlin, 1991.Google Scholar
  5. [Cla77]
    M. R. B. Clarke. A Quantitative Study of King and Pawn against King. In M. R. B. Clarke, editor, Advances in Computer Chess 1, pages 108–118, Edinburgh, Scotland, 1977. Edinburgh Univ. Press.Google Scholar
  6. [FI93]
    U. M. Fayyad and K. B. Irani. Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning. In 13th International Joint Conference on Artificial Intelligence, pages 1022–1027, San Mateo, 1993. Morgan Kaufmann Publ.Google Scholar
  7. [Hee84]
    A. Heeffer. Automated Acquisition of Concepts for the Description of Middle-Game Positions in Chess. Technical Report No. TIRM-84-005, The Turing Institute, 1984.Google Scholar
  8. [Hor84]
    H. Horacek. Some Conceptual Defects of Evaluation Functions. In T. O'Shea, editor, Proc. ECAI-84. Elsevier Science Publishers B.V., 1984.Google Scholar
  9. [HvdHS89]
    I. S. Herschberg, H. J. van den Herik, and P. N. A. Schoo. Verifying and Codifying Strategies in the KNNKP(h) Endgame. ICCA Journal, 12(3):144–154, 1989.Google Scholar
  10. [Kor84]
    J. Korst. Het genereren van regels voor schaak eindspelen ofwel eindspelen, moeilijker dan je denkt! Master's thesis, Technische Universität Delft, Delft, 1984.Google Scholar
  11. [Kur77]
    R. Kurz. Musterverarbeitung bei der Schachprogrammierung. PhD thesis, Universität Stuttgart, Stuttgart, 1977.Google Scholar
  12. [Mic77]
    D. Michie. King and Rook against King: Historical Background and a Problem on the Infinite Board. In M. R. B. Clarke, editor, Advances in Computer Chess 1, pages 30–59, Edinburgh, Scotland, 1977. Edinburgh Univ. Press.Google Scholar
  13. [MN77]
    R. S. Michalski and P. Negri. An Experiment on Inductive Learning in Chess End Games, pages 175–192. Halstead Press, Ellis Horwood, Chichester, UK, 1977.Google Scholar
  14. [Naj92]
    O. Najmann. Techniques and Heuristics for Acquiring Symbolic Knowledge from Examples. PhD thesis, Universität-Gesamthochschule-, Paderborn, 1992.Google Scholar
  15. [PFRS92]
    Chr. Posthoff, C. Friedrich, D. Rätz, and O. Schumann. Zur Compilation von Wissensbasen. PROKON-Memo Nr. 1, TU Chemnitz, 1992.Google Scholar
  16. [Pos92]
    Chr. Posthoff. Fuzzy Logics — New Concepts for Computer Chess? InH. J. van den Herik and V. Allis, editors, Heuristic Programming in Irtificial Intelligence 3. The Third Computer Olympiad, pages 88–101. Ellis Horwood, 1992.Google Scholar
  17. [PS94]
    Chr. Posthoff and M. Schlosser. Mengentheoretische Grundlagen für optimale Strategien beim Planen und Konfigurieren. In R. Bergmann, J. Paulokat, A.-M. Schoeller, and H. Wache, editors, Proc. 8. Workshop ”Planen und Konfigurieren”, Kaiserslautern, 18.–19. April 1994, pages 186–189. Universität und DFKI Kaiserslautern, 1994.Google Scholar
  18. [PSS92]
    Chr. Posthoff, M. Schlosser, and R. Staudte. Wissensdarstellung und-verarbeitung in strategischen Spielen. Preprint Nr. 218, Juni 1992, TU Chemnitz, 1992.Google Scholar
  19. [PSSZ94]
    Chr. Posthoff, M. Schlosser, R. Staudte, and J. Zeidler. Transformations of Knowledge. In H. J. van den Herik, I. S. Herschberg, and J. W. H. M. Uiterwijk, editors, Advances in Computer Chess 7, pages 177–202, Maastricht, The Netherlands, 1994. University of Limburg.Google Scholar
  20. [PSZ93a]
    Chr. Posthoff, M. Schlosser, and J. Zeidler. Optimal strategies. In Proc. First European Congress on Fuzzy and Intelligent Technologies (EU-FIT'93), Aachen, September 7–10, pages 643–644, Aachen, 1993.Google Scholar
  21. [PSZ93b]
    Chr. Posthoff, M. Schlosser, and J. Zeidler. Search vs. Knowledge?-Search and Knowledge! In Proc. 3rd KADS Meeting, March 8–9 1993, pages 305–326, Munich, 1993. SIEMENS AG, Corporate Research and Development.Google Scholar
  22. [Qui83]
    J. R. Quinlan. Learning Efficient Classification Procedures and their Application to Chess End Games, pages 463–482. Morgan Kaufmann, Los Altos, Cal., 1983.Google Scholar
  23. [Roy86]
    A. J. Roycroft. GBR Class 0023. EG, 6(83):12–15, 1986.Google Scholar
  24. [Sch88]
    M. Schlosser. Computers and Chess Problem Composition. ICCA Journal, 11(4):51–55, 1988.Google Scholar
  25. [Sch91]
    M. Schlosser. Can a Computer Compose Chess Problems? In D. F. Beal, editor, Advances in Computer Chess 6, pages 117–131, Chichester, UK, 1991. Ellis Horwood.Google Scholar
  26. [Sch92]
    M. Schlosser. A Test-Bed for Investigations in Machine Learning. Gosler-Report No. 18, TH Leipzig, October 1992.Google Scholar
  27. [Sch94]
    O. Schumann. Darstellung und Verarbeitung regelorientierter Wissensbasen mittels Boole scher Gleichungen. PhD thesis, TU ChemnitzZwickau, FB Informatik, Chemnitz, April 1994.Google Scholar
  28. [Sei86]
    R. Seidel. Deriving Correct Pattern Descriptions and Rules for the KRK Endgame by Deductive Methods. In D. F. Beal, editor, Advances in Computer Chess 4, pages 19–36, Oxford, UK, 1986. Pergamon Press.Google Scholar
  29. [Ste84]
    D. Steinwender. Bewertungsfunktionen in Schachprogrammen. Master's thesis, Fachbereich Informatik, Universität Hamburg, Hamburg, 1984.Google Scholar
  30. [Str70]
    T. Ströhlein. Untersuchungen über kombinatorische Spiele. PhD thesis, TU München, München, 1970.Google Scholar
  31. [Val84]
    L. G. Valiant. A Theory of the Learnable. Communications of the ACM, 27(11):1134–1142, 1984.Google Scholar
  32. [Zer12]
    E. Zermelo. Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. In 5. Int. Mathematikerkongreβ, volume 2, pages 501–504, Cambridge, 1912.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Christian Posthoff
    • 1
  • Michael Schlosser
    • 2
  1. 1.Dept. of Mathematics and Computer ScienceUniversity of The West IndiesSt. AugustineTrinidad & Tobago
  2. 2.Fakultät für InformatikTechnische Universität Chemnitz-ZwickauChemnitzGermany

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