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On the complexity of proof deskolemization

Published online by Cambridge University Press:  12 March 2014

Matthias Baaz ,
Stefan Hetzl  and
Daniel Weller
Matthias Baaz
Affiliation:
Institute of Discrete Mathematics and Geometry (E104), Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria, E-mail: [email protected]
Stefan Hetzl
Affiliation:
Laboratoire Preuves, Programmes et Systèmes (PPS), Université Paris Diderot – Paris 7, 175 Rue du Chevaleret, 75013 Paris, France, E-mail: [email protected]
Daniel Weller
Affiliation:
Institute of Computer Languages (E185), Vienna University of Technology, Favoritenstraβe 9, 1040 Vienna, Austria, E-mail: [email protected]
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Abstract

We consider the following problem: Given a proof of the Skolemization of a formula F, what is the length of the shortest proof of F? For the restriction of this question to cut-free proofs we prove corresponding exponential upper and lower bounds.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 669 - 686
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[1] Avigad, Jeremy, Eliminating definitions and Skolem functions in first-order logic, ACM Transactions on Computational Logic, vol. 4 (2003), no. 3, pp. 402–415.Google Scholar
[2] Baaz, Matthias and Leitsch, Alexander, Skolemization and proof complexity, Fundamenta Informaticae, vol. 20 (1994), no. 4, pp. 353–379.Google Scholar
[3] Baaz, Matthias and Leitsch, Alexander, Cut normalforms and proof complexity, Annals of Pure and Applied Logic, vol. 97 (1999), pp. 127–177.CrossRefGoogle Scholar
[4] Baaz, Matthias and Leitsch, Alexander, Cut-elimination and redundancy-elimination by resolution, Journal of Symbolic Computation, vol. 29 (2000), no. 2, pp. 149–176.Google Scholar
[5] Clote, Peter and Krajíček, Jan, Open problems, Arithmetic, proof theory and computational complexity (Clote, Peter and Krajíček, Jan, editors), Oxford University Press, 1993, pp. 1–19.Google Scholar
[6] Gentzen, Gerhard, Untersuchungen über das logische Schlieβen II, Mathematische Zeitschrift, vol. 39 (1935), no. 1, pp. 405–431.CrossRefGoogle Scholar
[7] Hähnle, Reiner and Schmitt, Peter H., The liberalized δ-rule in free variable semantic tableaux, Journal of Automated Reasoning, vol. 13 (1994), no. 2, pp. 211–221.Google Scholar
[8] Hilbert, David and Bernays, Paul, Grundlagen der Mathematik II, 2nd ed., Springer, 1970.Google Scholar
[9] Miller, Dale, A compact representation of proofs, Studia Logica, vol. 46 (1987), no. 4, pp. 347–370.Google Scholar
[10] Statman, Richard, Lower bounds on Herbrand's theorem, Proceedings of the American Mathematical Society, vol. 75 (1979), pp. 104–107.Google Scholar
[11] Troelstra, A. S. and Schwichtenberg, H., Basic proof theory, second ed., Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 2000.Google Scholar