Completeness criterion with respect to the enumeration closure operator in the three-valued logic

References

[1] Danil’chenko A. F., “Parametric expressibility of functions of three-valued logic”, Algebra i logika, 16, 1977, 266–280 (in Russian).10.1007/BF01669278Search in Google Scholar

[2] Danil’chenko A.F., “Parametrically closed classes of three-valued logic functions”, Izv. ANMSSR, 2 (1978), 13–20 (in Russian).Search in Google Scholar

[3] Kuznetsov A.V., “On the means for detecting non-deducibility and inexpressibility”, Logicheskii vyvod, M.: Nauka, 1979, 5–33 (in Russian).Search in Google Scholar

[4] Marchenkov S.S., “Basic relations of the S-classification of functions of the multi-valued logic”, Discrete Math. Appl., 6:2 (1996), 149–178.10.1515/dma.1996.6.2.149Search in Google Scholar

[5] Marchenkov S.S., “On expressibility of functions of many-valued logic in some logical-functional languages”, Discrete Math. Appl., 9:6 (1999), 563–581.10.1515/dma.1999.9.6.563Search in Google Scholar

[6] Marchenkov S.S., S-classification of functions of the multi-valued logic, M.: Fizmatlit, 2001 (in Russian), 80 pp.Search in Google Scholar

[7] Marchenkov S.S., “Discriminatory classes of three-valued logic”, Matematicheskie voprosy kibernetiki, 2003, №12, 15–26 (in Russian).Search in Google Scholar

[8] Marchenkov S.S., “Criterion for positive completeness in three-valued logic”, Diskretnyy analiz i issledovanie operatsiy, 13:3 (2006), 27–39 (in Russian).Search in Google Scholar

[9] Marchenkov S.S., “Definition of positively closed classes by endomorphism semigroups”, Discrete Math. Appl., 22:5-6 (2012), 511–520.10.1515/dma-2012-035Search in Google Scholar

[10] Marchenkov S.S., “On the enumeration closure operator in multivalued logic”, Moscow Univ. Comput. Math. and Cybernet., 39:2 (2015), 81–87.10.3103/S0278641915020053Search in Google Scholar

[11] Marchenkov S.S., Strong closure operators, M.: MAKS Press, 2017 (in Russian), 93 pp.Search in Google Scholar

[12] Marchenkov S.S., “Extensions of the positive closure operator by means of logical connectives”, J. Appl. Industr.Math., 12:4 (2018), 678–683.10.1134/S1990478918040087Search in Google Scholar

[13] Nguen Van Khoa, “On the structure of self-dual closed classes of three-valued logic P₃”, Discrete Mathematics, 4:4 (1992), 82–95 (in Russian).Search in Google Scholar

[14] Tarasova O.S., “Classes of k-valued logic closed under the extended operation of superposition”, Moscow Univ. Bulletin. Ser. 1. Math., mech., 2001, №6, 54–57 (in Russian).Search in Google Scholar

[15] Tarasova O.S., “Classes of functions of three-valued logic, closed under the operations of superposition and permutation”, Moscow Univ. Bulletin. Ser. 1. Math., mech., 2004, №1, 25–29 (in Russian).Search in Google Scholar

[16] Yablonskii S. V., “Functional constructions in a k-valued logic”, Trudy Mat. Inst. imeni V. A. Steklova, 51, 1958, 5–142 (in Russian).Search in Google Scholar

[17] Yanov Yu.I., Muchnik A.A., “On the existence of k-valued closed classes without a basis”, Doklady AN SSSR, 127:1 (1959), 44–46.Search in Google Scholar

[18] Danil’chenko A. F., “On parametrical expressibility of the functions of k-valued logic”, Colloq. Math. Soc. J.Bolyai, 28 (1981), 147–159.Search in Google Scholar