NDLI: A New Normalization Strategy for the Implicational Fragment of Classical Propositional Logic

Content Provider	Springer Nature Link
Author	Pereira, Luiz C. Haeusler, Edward H. Costa, Vaston G. Sanz, Wagner
Copyright Year	2010
Abstract	The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce’s formula (((A → B) → A) → A). E. Zimmermann [6] has shown how to extend Prawitz’ normalization strategy to Peirce’s rule: applications of Peirce’s rule can be restricted to atomic conclusions. The aim of the present paper is to extend Seldin’s normalization strategy to Peirce’s rule by showing that every derivation Π in the implicational fragment can be transformed into a derivation Π′ such that no application of Peirce’s rule in Π′ occurs above applications of →-introduction and →-elimination. As a corollary of Seldin’s normalization strategy we obtain a form of Glivenko’s theorem for the classical {→}-fragment.
Starting Page	95
Ending Page	108
Page Count	14
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	96
Issue Number	1
e-ISSN	15728730
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-08-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Natural Deduction Peirce’s Rule Normalization Computational Linguistics Mathematical Logic and Foundations Logic
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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