Geodesic
Deduction normalization theorem for Sette's logic and its modifications
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2019), pp. 26-33
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2019},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a4/}
}
TY  - JOUR
AU  - Ya. I. Petrukhin
TI  - Deduction normalization theorem for Sette's logic and its modifications
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 26
EP  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a4/
LA  - ru
ID  - VMUMM_2019_1_a4
ER  - 
%0 Journal Article
%A Ya. I. Petrukhin
%T Deduction normalization theorem for Sette's logic and its modifications
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 26-33
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_1_a4/
%G ru
%F VMUMM_2019_1_a4
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/

[1] Lewin R. A., Mikenberg I. F., “Literal-paraconsistent and literal-paracomplete matrices”, Math. Log. Quart., 52:5 (2006), 478–493 | DOI | MR | Zbl

[2] Priest G., “Paraconsistent logic”, Handbook of philosophical logic, v. 6, 2nd ed., eds. D. M. Gabbay, F. Guenthner, Kluwer Academic Publishers, 2002, 287–393 | DOI | MR

[3] Sette A. M., Carnielli W. A., “Maximal weakly-intuitionistic logics”, Stud. Log., 55:1 (1995), 181–203 | DOI | MR | Zbl

[4] Karpenko A., Tomova N., “Bochvar's three-valued logic and literal paralogics: Their lattice and functional equivalence”, Log. and Log. Phil., 26:2 (2017), 207–235 | MR | Zbl

[5] Karpenko A. S., Tomova N. E., Trekhznachnaya logika Bochvara i literalnye paralogiki, IF RAN, M., 2016

[6] Sette A. M., “On propositional calculus P$ _{1} $”, Math. Jap., 18:3 (1973), 173–180 | MR | Zbl

[7] Carnielli W. A., Marcos J., “A Taxonomy of C-systems”, Paraconsistency: The Logical Way to the Inconsistent, eds. W. A. Carnielli, M. E. Coniglio, I. M. L. D'Ottaviano, Marcel Dekker, N.Y., 2002, 1–94 | MR | Zbl

[8] Popov V. M., “Ob odnoi trekhznachnoi parapolnoi logike”, Log. Invest., 9 (2002), 175–178 | Zbl

[9] Marcos J., “On a problem of da Costa”, Essays of the foundations of mathematics and logic, v. 2, ed. G. Sica, Polimetrica, Monza, 2005, 53–69 | Zbl

[10] Bochvar D. A., “Ob odnom trekhznachnom ischislenii i ego primenenii k analizu paradoksov klassicheskogo rasshirennogo funktsionalnogo ischisleniya”, Matem. sb., 4:2 (1938), 287–308

[11] Karpenko A. S., “A maximal paraconsistent logic: The combination of two three-valued isomorphs of classical logic”, Frontiers of Paraconsistent Logic, eds. D. Batens, C. Mortensen, G. Priest, J.-P. van Bendegem, Research Studies Press, Baldock, 2002, 181–187 | MR

[12] Popov V. M., “On the logics related to Arruda's system V1”, Log. and Log. Phil., 7 (1999), 87–90 | DOI | MR | Zbl

[13] Carnielli W. A., Lima-Marques M., “Society semantics and multiple-valued logics”, Adv. Contemp. Log. and Comput. Sci., 235 (1999), 33–52 | DOI | MR | Zbl

[14] Ciuciura J., “Paraconsistency and Sette's calculus P1”, Log. and Log. Phil., 24:2 (2015), 265–273 | MR | Zbl

[15] Ciuciura J., “A weakly-intuitionistic logic I1”, Log. Invest., 21:2 (2015), 53–60 | MR | Zbl

[16] Gentzen G., “Untersuchungen über das logische Schliessen I; II”, Math. Z., 39:1 (1935), 176–210 ; 405–431 | DOI | MR

[17] Jaśkowski S., “On the rules of suppositions in formal logic”, Stud. Log., 1 (1934), 5–32

[18] Becchio D., Pabion J-F., “Gentzen's techniques in the three-valued logic of Łukasiewicz”, J. Symb. Log., 42:2 (1977), 123–124

[19] Łukasiewicz J., “O logice trójwartościowej”, Ruch Fil., 5 (1920), 170–171

[20] Petrukhin Y., “Natural deduction for three-valued regular logics”, Log. and Log. Phil., 26:2 (2017), 197–206 | MR | Zbl

[21] Petrukhin Y., “Natural deduction for four-valued both regular and monotonic logics”, Log. and Log. Phil., 27:1 (2018), 53–66 | MR | Zbl

[22] Petrukhin Y., “Natural deduction for Fitting's four-valued generalizations of Kleene's logics”, Logica Universalis, 11:4 (2017), 525–532 | DOI | MR | Zbl

[23] Petrukhin Ya. I., “Sistema naturalnogo vyvoda dlya trekhznachnoi logiki Geitinga”, Vestn. Mosk. un-ta. Matem. Mekhan., 2017, no. 3, 63–66 | MR | Zbl

[24] Petrukhin Ya. I., “Naturalnye ischisleniya dlya trekhznachnykh logik bessmyslennosti Z i E”, Vestn. Mosk. un-ta. Matem. Mekhan., 2018, no. 1, 60–63 | MR | Zbl

[25] Arieli O., Avron A., Zamansky A., What is an ideal logic for reasoning with inconsistency?, Proc. IJCAI'11 (Barcelona, 2011), 706–711

[26] Zimmermann E., “Peirce's rule in natural deduction”, Theor. Comput. Sci., 275:1–2 (2002), 561–574 | DOI | MR | Zbl

[27] Kooi B., Tamminga A., “Completeness via correspondence for extensions of the logic of paradox”, Rev. Symb. Log., 5:4 (2012), 720–730 | DOI | MR | Zbl

[28] van Dalen D., Logic and Structure, 3rd ed., Springer-Verlag, Berlin, 1997 | MR

[29] Prawitz D., Natural Deduction. A Proof-Theoretical Study, Almquist and Wiksell, Stockholm, 1965 | MR | Zbl