A complete, nonredundant algorithm for reversed skolemization

  • P. T. Cox
  • T. Pietrzykowski
Friday Afternoon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 87)


An algorithm is presented which, for an arbitrary literal containing Skolem functions, outputs a set of closed quantified literals with the following properties. If a and b are formulae we define a ⊃ b iff {sk(a),dsk(b)} is unifiable where sk denotes Skolemization and dsk denotes the dual operation, where the roles of ∀ and ∃ are reversed. If d is an arbitrary literal and X is the output, then:
  1. (i)

    Soundness: if x ∈ X then x ⊃ d

  2. (ii)

    Completeness: if a ⊃ d then ∃x ∈ X such that a ⊃ x

  3. (iii)

    Nonredundancy: if x,y ∈ X then x ⊅ y and y ⊅ x.



Free Variable Quantifier String Dual Operation Skolem Function Major Loop 
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. [1]
    Bledsoe, W.W., and Ballantyne, A.M., "Unskolemizing", Mathematics Dept. Memo ATP-41, University of Texas, July 1978.Google Scholar
  2. [2]
    Cox, P.T. and Pietrzykowski, T., On reverse Skolemization, Research Report CS-80-01, Department of Computer Science, University of Waterloo, 1980.Google Scholar
  3. [3]
    Pietrzykowski, T., Mechanical Hypothesis Formation, Research Report CS-78-33, Department of Computer Science, University of Waterloo, 1978.Google Scholar
  4. [4]
    Skolem, T., Über die mathematische Logik, Norsk mathematisk Tidskrift, 10, pp. 125–142, 1928.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • P. T. Cox
    • 1
  • T. Pietrzykowski
    • 2
  1. 1.University of AucklandNew Zealand
  2. 2.University of Waterloo, Acadia UniversityCanada

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