Towards first-order deduction based on Shannon graphs

  • Joachim Posegga
  • Bertram Ludäscher
Technical Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 671)


We present a new approach to Automated Deduction based on the concept of Shannon graphs, which are also known as Binary Decision Diagrams (BDDs). A Skoleinized formula is first transformed into a Shannon graph, then the latter is compiled into a set of Horn clauses. These can finally be run as a Prolog program trying to refute the initial formula. It is also possible to precompile axiomatizations into Prolog and load these theories as required.


Automated Deduction Shannon Graphs Binary Decision Diagrams 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Brace et al., 1990]
    Karl S. Brace, Richard L. Rudell, & Randal E. Bryant. Efficient implementation of a BDD package. In Proc. 27 th ACM/IEEE Design Automation Conference, pages 40–45. IEEE Press, 1990.Google Scholar
  2. [Bryant, 1986]
    Randal Y. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, C-35:677–691, 1986.Google Scholar
  3. [Kemper et al., 1992]
    A. Kemper, G. Moerkotte, & M. Steinbrunn. Optimization of boolean expressions in object bases. In Proc. Intern. Conf. on Very Large Databases, 1992.Google Scholar
  4. [Kropf & Wunderlich, 1991]
    T. Kropf & H.-J. Wunderlich. A common approach to test generation and hardware verification based on temporal logic. In Proc. Intern. Test Conf., pages 57–66, Nashville, TN, October 1991.Google Scholar
  5. [Lee, 1959]
    C. Lee. Representation of switching circuits by binary decision diagrams. Bell System Technical Journal, 38:985–999, 1959.Google Scholar
  6. [Orlowska, 1969]
    Ewa Orlowska. Automatic theorem proving in a certain class of formulae of predicate calculus. Bull. de L'Acad. Pol. des Sci., Série des sci. math., astr. et phys., XVII(3):117–119, 1969.Google Scholar
  7. [Posegga, 1992]
    Joachim Posegga. First-order shannon graphs. In Proc. Workshop on Automated Deduction / Intern. Conf. on Fifth Generation Computer Systems, ICOT TM-1184, Tokyo, Japan, June 1992.Google Scholar
  8. [Shannon, 1938]
    C. E. Shannon. A symbolic analysis of relay and switching circuits. AIEE Transactions, 67:713–723, 1938.Google Scholar
  9. [Stickel, 1988]
    Mark E. Stickel. A Prolog Technology Theorem Prover. In E. Lusk & R. Overbeek, editors, 9th International Conference on Automated Deduction, Argonne, Ill., May 1988. Springer-Verlag.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Joachim Posegga
    • 1
  • Bertram Ludäscher
    • 1
  1. 1.Institut für Logik, Komplexität und DeduktionssystemeUniversität KarlsruheKarlsruheGermany

Personalised recommendations