Geodesic
Closed classed of three-valued logic that contain essentially multiplace functions
Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 98-107.

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

All 23 closed classes of three-valued logic that contain essentially multiplace linear functions are defined. It is shown that the order of every such class is not greater than 3.
Keywords: three-valued logic, closed classes, linear functions. 
@article{DM_2015_27_1_a6,
     author = {S. S. Marchenkov},
     title = {Closed classed of three-valued logic that contain essentially multiplace functions},
     journal = {Diskretnaya Matematika},
     pages = {98--107},
     publisher = {mathdoc},
     volume = {27},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_1_a6/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - Closed classed of three-valued logic that contain essentially multiplace functions
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 98
EP  - 107
VL  - 27
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_1_a6/
LA  - ru
ID  - DM_2015_27_1_a6
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T Closed classed of three-valued logic that contain essentially multiplace functions
%J Diskretnaya Matematika
%D 2015
%P 98-107
%V 27
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_1_a6/
%G ru
%F DM_2015_27_1_a6
S. S. Marchenkov. Closed classed of three-valued logic that contain essentially multiplace functions. Diskretnaya Matematika, Tome 27 (2015) no. 1, pp. 98-107. http://geodesic.mathdoc.fr/item/DM_2015_27_1_a6/

[1] Danilchenko, A. F., “O parametricheskoi vyrazimosti funktsii trekhznachnoi logiki”, Algebra i logika, 16:4 (1977), 397–416 | MR | Zbl

[2] Danilchenko, A. F., “Parametricheski zamknutye klassy funktsii trekhznachnoi logiki”, Izvestiya AN MSSR, 2 (1979), 13–20

[3] Marchenkov, S. S., “O zamknutykh klassakh samodvoistvennykh funktsii mnogoznachnoi logiki”, Problemy kibernetiki, 36 (1979), 5–22 | MR | Zbl

[4] Marchenkov, S. S., “Odnorodnye algebry”, Problemy kibernetiki, 39 (1982), 85–106 | MR | Zbl

[5] Marchenkov, S. S., “O zamknutykh klassakh samodvoistvennykh funktsii mnogoznachnoi logiki II”, Problemy kibernetiki, 40 (1983), 261–266 | MR | Zbl

[6] Marchenkov, S. S., “O zamknutykh klassakh v $P_k$, soderzhaschikh odnorodnye funktsii”, Preprint IPM im. M. V. Keldysha AN SSSR, 1984, no. 35, 1–28 | MR

[7] Marchenkov, S. S., “Klonovaya klassifikatsiya dualno diskriminatornykh algebr s konechnym nositelem”, Matematicheskie zametki, 61:3 (1997), 359–366 | DOI | MR | Zbl

[8] Marchenkov S. S., $S$-klassifikatsiya funktsii trekhznachnoi logiki, Fizmatlit, Moskva, 2001, 79 pp. | Zbl

[9] Marchenkov, S. S., “Diskriminatornye klassy trekhznachnoi logiki”, Matematicheskie voprosy kibernetiki, 12 (2003), 15–26

[10] Marchenkov, S. S., “O poryadkakh diskriminatornykh klassov mnogoznachnoi logiki”, Matematicheskie zametki, 86:4 (2009), 550–556 | DOI | MR | Zbl

[11] Marchenkov, S. S., Demetrovich, Ya., Khannak, Ya., “O zamknutykh klassakh samodvoistvennykh funktsii v $P_3$”, Metody diskretnogo analiza v reshenii kombinatornykh zadach, 1980, no. 34, 38–73 | MR | Zbl

[12] Nagornyi, A. S., “O raspredelenii trekhznachnykh funktsii po predpolnym klassam”, Vestnik Moskovskogo un-ta. Seriya 15. Vychisl. matem. i kibernetika, 2012, no. 3, 45–52 | MR

[13] Nguen Van Khoa, “O strukture samodvoistvennykh zamknutykh klassov trekhznachnoi logiki $P_3$”, Diskretnaya matematika, 4:4 (1992), 82–95 | MR

[14] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 1986, 384 pp. | MR

[15] Bagynszki, J., Demetrovics, J., “The lattice of linear classes in prime-valued logics”, Banach Center Publ., 7 (1982), 105–123 | MR

[16] Baker, A., Pixley, A. F., “Polynomial interpolation and the Chinese Remainder Theorem for algebraic systems”, Math. Zeitschrift, 143 (1975), 165–174 | DOI | MR | Zbl

[17] Csakany, B., “All minimal clones on three-element set”, Acta Cybernet., 6:3 (1983), 227–238 | MR | Zbl

[18] Lau, D., “Bestimmung der Ordnung maximaler Klassen von Funktionen der $k$-vertigen Logik”, Z. Math. Logik Grundlag. Math., 24:1 (1978), 79–96 | DOI | MR | Zbl