Abstract
The methods of this paper can be applied as well to intuitionistic proof systems like Natural Deduction. It is obvious that the application of extended reductions similar to projections will result in a loss of confluence; on the other hand, confluence is of doubtful value if the complexity of cut-elimination is the main concern.
Preview
Unable to display preview. Download preview PDF.
References
Baaz, M., Leitsch, A.: On skolemization and proof complexity Fundamenta Informaticae, 20/4, pp. 353–379 (1994).
Baaz, M., Leitsch, A.: Cut Normal Forms and Proof Complexity, Technical Report TR-CS-BL-96-1, Institut für Computersprachen, TU Wien (1996).
Gentzen, G.: Untersuchungen über das logische Schließen, Mathematische Zeitschrift 39, pp. 176–210, pp. 405–431 (1934–1935).
Goad, C.A.: Computational Uses of the Manipulation of Formal Proofs, Ph.D. Thesis, Stanford University (1980)
Orevkov, V.P.: Lower bounds for increasing complexity of derivations after cut-elimination (translation), Journal of Soviet Mathematics, pp. 2337–2350 (1982).
Schwichtenberg, H.: Proof Theory: Some Applications of Cut-Elimination, in Handbook of Mathematical Logic, John Barwise (ed.), North-Holland, Amsterdam, 5th printing, (1989).
Statman, R.: Lower bounds on Herbrand's theorem, in Proc. of the Amer. Math. Soc. 75, pp. 104–107, (1979).
Takeuti, G.: Proof Theory, North-Holland, Amsterdam, 2nd edition, (1987).
Author information
Authors and Affiliations
Corresponding author
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baaz, M., Leitsch, A. (1997). Fast cut-elimination by projection. In: van Dalen, D., Bezem, M. (eds) Computer Science Logic. CSL 1996. Lecture Notes in Computer Science, vol 1258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63172-0_30
Download citation
DOI: https://doi.org/10.1007/3-540-63172-0_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63172-9
Online ISBN: 978-3-540-69201-0
eBook Packages: Springer Book Archive