On implicit extensions in many-valued logic

References

[1] Danil’chenko A. F., “Parametric expressibility of functions of three-valued logic”, Algebra and Logic, 16:4 (1977), 397–416 (in Russian).10.1007/BF01669278Search in Google Scholar

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

[3] Kasim-Zade O. M., “On the implicit expressibility of Boolean functions”, Vestnik MGU. Ser. 1: Matem., mekhanika, 2 (1995), 7–20 (in Russian).Search in Google Scholar

[4] Kasim-Zade O. M., “Implicit expressibility in two-valued logic and crypto-isomorphisms of two-element algebras”, Dokl. Math., 53:3 (1996), 366–368.Search in Google Scholar

[5] Kasim-Zade O. M., “On implicit forms of expressibility in multivalued logics”, Proc. All-Russian Conf. «Discrete Analysis and Operations Research» (Novosibirsk, June 2004), 2004, 32–35 (in Russian).Search in Google Scholar

[6] Kasim-Zade O. M., “Implicit completeness in k -valued logic”, Mosc. Univ. Math. Bull., 62:3 (2007), 90–94.10.3103/S0027132207030023Search in Google Scholar

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

[8] Marchenkov S. S., “Homogeneous algebras”, Problemy kibernetiki, 39 (1982), 85–106 (in Russian).Search in Google Scholar

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

[10] Marchenkov S. S., Closure operators of the logical-functional type, M.: MAKS Press, 2012 (in Russian), 99 pp.Search in Google Scholar

[11] Marchenkov S. S., Strong closure operators, M.: Fizmatlit, 2017 (in Russian), 94 pp.Search in Google Scholar

[12] Marchenkov S. S., “Implicit expressibility in multivalued logic”, Vestnik MGU. Ser. 15: Vychisl. matem. i kibern., 3 (2022), 41–48 (in Russian).10.3103/S0278641922030086Search in Google Scholar

[13] Orekhova E. A., “On a criterion for implicit completeness in k-valued logic”, Matematicheskie voprosy kibernetiki, 11 (2002), 77–90 (in Russian).Search in Google Scholar

[14] Orekhova E. A., “A criterion for the implicit Sheffer property in three-valued logic”, Diskretn. Anal. Issled. Oper. Ser. 1, 10, 2003, 82–105 (in Russian).Search in Google Scholar

[15] Orekhova E. A., “On one criterion of implicit completeness in three-valued logic”, Matematicheskie voprosy kibernetiki, 12 (2003), 27–74 (in Russian).Search in Google Scholar

[16] Starostin M. V., “Implicitly maximal classes and implicit completeness criterion in the three-valued logic”, Moscow Univ. Math. Bull., 73:2 (2018), 82–84.10.3103/S0027132218020067Search in Google Scholar

[17] Starostin M. V., “Some implicitly precomplete classes of functions of three-valued logic preserving subsets.”, Moscow Univ. Math. Bull., 73:6 (2018), 245–248.10.3103/S0027132218060050Search in Google Scholar

[18] Starostin M. V., “On some implicitly precomplete classes of monotone functions in P_k”, Discrete Math. Appl., 30:1 (2020), 45–51.10.1515/dma-2020-0005Search in Google Scholar

[19] Yanov Yu. I., Muchnik A. A., “On the existence of k-valued closed classes having no finite basis”, Dokl. Akad. Nauk SSSR, 127:1 (1959), 44–46 (in Russian).Search in Google Scholar

[20] Burris S., Willard R., “Finitely many primitive positive clones”, Proc. Amer. Math. Soc., 101:3 (1987), 427–430.10.1090/S0002-9939-1987-0908642-5Search in Google Scholar

[21] Danil’čenko 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