Abstract
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:
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(i)
Soundness: if x ∈ X then x ⊃ d
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(ii)
Completeness: if a ⊃ d then ∃x ∈ X such that a ⊃ x
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(iii)
Nonredundancy: if x,y ∈ X then x ⊅ y and y ⊅ x.
This work was supported by NSERC Grants: A3025 and A5267.
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Bibliography
Bledsoe, W.W., and Ballantyne, A.M., "Unskolemizing", Mathematics Dept. Memo ATP-41, University of Texas, July 1978.
Cox, P.T. and Pietrzykowski, T., On reverse Skolemization, Research Report CS-80-01, Department of Computer Science, University of Waterloo, 1980.
Pietrzykowski, T., Mechanical Hypothesis Formation, Research Report CS-78-33, Department of Computer Science, University of Waterloo, 1978.
Skolem, T., Über die mathematische Logik, Norsk mathematisk Tidskrift, 10, pp. 125–142, 1928.
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© 1980 Springer-Verlag Berlin Heidelberg
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Cox, P.T., Pietrzykowski, T. (1980). A complete, nonredundant algorithm for reversed skolemization. In: Bibel, W., Kowalski, R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10009-1_28
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DOI: https://doi.org/10.1007/3-540-10009-1_28
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