Abstract
We present a new manageable formulation of natural deduction with a rule of existential instantiation ∃xA[x]/A[b]. It simplifies skolemizing devices of earlier formulations, includes a new rule for disjunction and admits a proof of strong normalization. This opens way to the treatment of new systems for which only normal form theorems are known.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Gentzen G.: Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39 (1934) 176–210, 405–431
Girard J.-Y., Lafont Y., Taylor P.: Proofs and Types, Cambridge University Press, Cambridge (1988)
Leivant D.: Existential instantiation in a system of natural deduction, Mathematish Centrum-ZW 13–73 (1973)
Mints G.: Lewis Systems and the System T. In Mints G.: Selected Papers in Proof Theory, North-Holland-Bibliopolis (1993), 221–294 (Russian Original 1974)
Mints G.: A Normal Form Theorem for Second-order Classical Logic with an Axiom of Choice, Math. USSR Izvestiya 32 N3 (1989) 587–605
Mints G.: Normal Deduction in the Intuitionistic Linear Logic, CSLI report, (1996)
Prawitz D.: Natural Deduction, Almquist and Wiksell (1965)
Prawitz D.: Ideas and Results in Proof Theory, In Proc. 2-nd Scand.Logic Symp., North-Holland, (1972) 235–308
Quine W.V.: On natural deduction, Journal of Symbolic Logic 15 (1950) 93–102
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mints, G. (1997). Existential instantiation and strong normalization. In: Adian, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 1997. Lecture Notes in Computer Science, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63045-7_26
Download citation
DOI: https://doi.org/10.1007/3-540-63045-7_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63045-6
Online ISBN: 978-3-540-69065-8
eBook Packages: Springer Book Archive