Geodesic
Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$
Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 45-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper, we prove the $\alpha$-completeness of finite systems of function of $k$-valued logic for $k=3,4$ containing all permutations of the symmetric group $S_k$ on the set $E_k=\{0,1,\dots,k-1\}$, the operation of addition modulo $k$, and $k$ certain binary operation. This result is extended to some other systems of functions which are obtained by replacing the operation of addition by some quasi-group operation. 
@article{DM_2006_18_4_a4,
     author = {A. L. Shabunin},
     title = {Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$},
     journal = {Diskretnaya Matematika},
     pages = {45--55},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_4_a4/}
}
TY  - JOUR
AU  - A. L. Shabunin
TI  - Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$
JO  - Diskretnaya Matematika
PY  - 2006
SP  - 45
EP  - 55
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2006_18_4_a4/
LA  - ru
ID  - DM_2006_18_4_a4
ER  - 
%0 Journal Article
%A A. L. Shabunin
%T Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$
%J Diskretnaya Matematika
%D 2006
%P 45-55
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2006_18_4_a4/
%G ru
%F DM_2006_18_4_a4
A. L. Shabunin. Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$. Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 45-55. http://geodesic.mathdoc.fr/item/DM_2006_18_4_a4/

[1] Glukhov M. M., “Ob $\alpha$-zamknutykh klassakh i $\alpha$-polnykh sistemakh funktsii $k$-znachnoi logiki”, Diskretnaya matematika, 1:1 (1989), 16–21

[2] Chernyshov A. L., “Usloviya $\alpha$-polnoty sistem funktsii mnogoznachnoi logiki”, Diskretnaya matematika, 4:4 (1992), 117–130 | MR

[3] Belousov V. D., Osnovy teorii kvazigrupp i lup, Nauka, Moskva, 1967

[4] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 1979