Geodesic
Deduction normalization theorem for Sette's logic and its modifications
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2019), pp. 26-33

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In this paper we formulate natural deduction systems for Sette's three-valued paraconsistent logic $\bf P^1$ and some related logics. For presented calculi we prove soundness, completeness, and normalization theorems. 
@article{VMUMM_2019_1_a4,
     author = {Ya. I. Petrukhin},
     title = {Deduction normalization theorem for {Sette's} logic and its modifications},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {26--33},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a4/}
}
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Ya. I. Petrukhin. Deduction normalization theorem for Sette's logic and its modifications. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2019), pp. 26-33. http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a4/