Note on resolution circuits

  • Zbigniew Stachniak
Communications Logic For Artificial Intelligence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 542)


In this paper we continue the study of the class of resolution logics initiated in [4–8]. The main result reported in the paper shows that there exists an effective method of associating with every resolution logic \(\mathcal{P}\)an AND-OR network \(\Re\)of resolution proof systems which is refutationally equivalent to \(\mathcal{P}\). Such AND-OR networks offer an attractive automated theorem proving representation for many resolution logics whose minimal resolution counterparts are much too big to be efficiently implemented.


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  1. [1]
    Grätzer, G. (1968). Universal Algebra. Van Nostrand.Google Scholar
  2. [2]
    Murray, N. (1982). Completely Non-Clausal Theorem Proving. Artificial Intelligence 18, 67–85.Google Scholar
  3. [3]
    Post, E. (1921). Introduction to a General Theory of Elementary Propositions. American Journal of Mathematics 43, 163–185.Google Scholar
  4. [4]
    Stachniak, Z. (1991). Extending Resolution to Resolution Logics. Journal of Experimental and Theoretical Artificial Intelligence 3, 17–32.Google Scholar
  5. [5]
    Stachniak, Z. (1991). Minimization of Resolution Proof Systems. Fundamenta Informaticae 14, 129–146.Google Scholar
  6. [6]
    Stachniak, Z. (1991). Resolution Approximation of First-Order Logics, to appear in Information and Computation.Google Scholar
  7. [7]
    Stachniak, Z. (1990). Note on Effective Constructibility of Resolution Proof Systems. Proceedings of the European Workshop on Logics in AI, JELIA ′90, Amsterdam, Lecture Notes in Artificial Intelligence 478, 487–498.Google Scholar
  8. [8]
    Stachniak, Z. (1988). Resolution Rule: An Algebraic Perspective. Proceedings of Algebraic Logic and Universal Algebra in Computer Science Conference, Ames, Lecture Notes in Computer Science 425, 227–242.Google Scholar
  9. [9]
    Wójcicki, R. (1988). Theory of Logical Calculi: Basic Theory of Consequence Operations. Kluwer Academic Publishers.Google Scholar
  10. [10]
    Zygmunt, J. (1983). An Application of the Lindenbaum Method in the Domain of Strongly Finite Sentential Calculi. Acta Universitatis Wratislaviensis 517, pp. 59–68.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Zbigniew Stachniak
    • 1
  1. 1.Department of Computer ScienceYork UniversityNorth YorkCanada

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