Normalization and excluded middle. I |
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Authors: | Jonathan P Seldin |
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Institution: | (1) Odyssey Research Associates and Department of Mathematics, Concordia University, Montréal, Québec, Canada |
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Abstract: | The usual rule used to obtain natural deduction formulations of classical logic from intuitionistic logic, namely
is stronger then necessary, and will give classical logic when added to minimal logic. A rule which is precisely strong enough
to give classical logic from intuitionistic logic, and which is thus exactly equivalent to the law of the excluded middle,
is
It is a special case of a version of Peirce's law:
In this paper it is shown how to normalize logics defined using these last two rules. Part I deals with propositional logics
and first order predicate logics. Part II will deal with first order arithmetic and second order logics.
This research was supported in part by grants EQ1648, EQ2908, and CE 110 of the program Fonds pour la Formation de Chercheurs
et l'aide à la Recherche (F.C.A.R.) of the Quèbec Ministry of Education. |
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Keywords: | |
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