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UNSOUND INFERENCES MAKE PROOFS SHORTER

Published online by Cambridge University Press:  14 March 2019

JUAN P. AGUILERA  and
MATTHIAS BAAZ
JUAN P. AGUILERA
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY VIENNA UNIVERSITY OF TECHNOLOGY WIEDNER HAUPTSTRAßE 8–10, 1040VIENNA, AUSTRIAE-mail: aguilera@logic.at
MATTHIAS BAAZ
Affiliation:
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY VIENNA UNIVERSITY OF TECHNOLOGY WIEDNER HAUPTSTRAßE 8–10, 1040VIENNA, AUSTRIAE-mail: baaz@logic.at
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Abstract

We give examples of calculi that extend Gentzen’s sequent calculus LK by unsound quantifier inferences in such a way that (i) derivations lead only to true sequents, and (ii) proofs therein are nonelementarily shorter than LK-proofs.

Keywords

03F0303F0503F07unsound inferencessequent calculuscut eliminationeigenvariable condition
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 1 , March 2019 , pp. 102 - 122
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

REFERENCES

Baaz, M. and Hetzl, S., On the non-confluence of cut-elimination, this Journal, vol. 76 (2011), pp. 313–340.Google Scholar
Baaz, M., Hetzl, S., and Weller, D., On the complexity of proof deskolemization, this Journal, vol. 77 (2012), pp. 669–686.Google Scholar
Baaz, M. and Leitsch, A., On skolemization and proof complexity. Fundamenta Informaticae, vol. 20 (1994), pp. 353–379.Google Scholar
Baaz, M. and Leitsch, A., Cut normal forms and proof complexity. Annals of Pure and Applied Logic, vol. 97 (1999), pp. 127–177.10.1016/S0168-0072(98)00026-8CrossRefGoogle Scholar
Hilbert, D. and Bernays, P., Grundlagen der Mathematik II, Springer-Verlag, Berlin, 1970.10.1007/978-3-642-86896-2CrossRefGoogle Scholar
Moser, G. and Zach, R., The epsilon calculus and Herbrand complexity. Studia Logica, vol. 82 (2006), no. 1, pp. 133–155.10.1007/s11225-006-6610-7CrossRefGoogle Scholar
Orevkov, V. P., Lower bounds for increasing complexity of derivations after cut elimination (in Russian). Journal of Soviet Mathematics, vol. 20 (1982), pp. 2337–2350.10.1007/BF01629444CrossRefGoogle Scholar
Statman, R., Lower bounds on Herbrand’s theorem. Proceedings of the American Mathematical Society, vol. 75 (1979), pp. 104–107.Google Scholar
Takeuti, G., Proof Theory, North-Holland, Amsterdam, 1980.Google Scholar