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About some symmetries of negation

Published online by Cambridge University Press:  12 March 2014

Brigitte Hösli  and
Gerhard Jäger
Brigitte Hösli
Affiliation:
Institute für Theoretische Informatik, ETH Zürich, CH-8092 Zürich, Switzerland, E-mail: [email protected]
Gerhard Jäger
Affiliation:
Institut für Informatik und Angewandte Mathematik, Universität Bern, CH-3012 Bern, Swizterland, E-mail: [email protected]
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Abstract

This paper deals with some structural properties of the sequent calculus and describes strong symmetries between cut-free derivations and derivations, which do not make use of identity axioms. Both of them are discussed from a semantic and syntactic point of view.

Identity axioms and cuts are closely related to the treatment of negation in the sequent calculus, so the results of this article explain some nice symmetries of negation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 473 - 485
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

[1] Girard, J.-Y., Proof theory and logical complexity, Volume I, Bibliopolis, Napoli, 1987.Google Scholar
[2] Girard, J.-Y., Lafont, Yves and Taylor, P., Proofs and types, Cambridge Tracts in Theoretical Computer Science, vol. 7, Cambridge University Press, Cambridge, 1989.Google Scholar
[3] Jäger, G., Some proof-theoretic aspects of logic programming, Logic and algebra of specification (Bauer, F. L., Brauer, W., and Schwichtenberg, H., editors), Springer, Berlin, 1993.Google Scholar
[4] Jäger, G., A deductive approach to logic programming, Research Report Universität Bern (1993).Google Scholar
[5] Kunen, K., Negation in logic programming, Journal of Logic Programming, vol. 4 (1987).CrossRefGoogle Scholar
[6] Schütte, K., Proof theory, Springer, Berlin, 1977.CrossRefGoogle Scholar
[7] Stärk, R. F., A complete axiomatization of the three-valued completion of logic programs, Journal of Logic and Computation, vol. 1 (1991).CrossRefGoogle Scholar
[8] Takeuti, G., Proof theory, (2nd edition), North-Holland, Amsterdam, 1987.Google Scholar