Abstract
Firstly, a natural deduction system in standard style is introduced for Nelson's para-consistent logic N4, and a normalization theorem is shown for this system. Secondly, a natural deduction system in sequent calculus style is introduced for N4, and a normalization theorem is shown for this system. Thirdly, a comparison between various natural deduction systems for N4 is given. Fourthly, a strong normalization theorem is shown for a natural deduction system for a sublogic of N4. Fifthly, a strong normalization theorem is proved for a typed λ-calculus for a neighbor of N4. Finally, it is remarked that the natural deduction frameworks presented can also be adapted for Wansing's basic connexive logic C.
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DOI 10.3166/jancl.15.405-435
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References found in this work BETA

Constructible Falsity and Inexact Predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
On the Representation of N4-Lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.

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