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Diskr. Mat., 1999, Volume 11, Issue 4, Pages 110–126 (Mi dm400)  

This article is cited in 23 scientific papers (total in 23 papers)

On the expressibility of functions of many-valued logic in some logical-functional classes

S. S. Marchenkov


Abstract: For each $k$, $k\ge2$, three logical-functional languages are introduced for the set of functions of $k$-valued logic: the positive expressibility language $\operatorname{Pos}_k$, the first-order language $1\operatorname{L}_k$, and the second-order language $2\operatorname{L}_k$. On the basis of the notion of expressibility in a language, the corresponding closure operators are defined. It is proved that the operators of $1\operatorname{L}_k$-closure and $2\operatorname{L}_k$-closure coincide. The $1\operatorname{L}_k$-closed and $\operatorname{Pos}_k$-closed classes are described with the help of symmetric groups and symmetric semigroups. The expressibility in the languages $1\operatorname{L}_k$ and $\operatorname{Pos}_k$ is compared with the parametric expressibility and the expressibility by terms.
The research was supported by the Russian Foundation for Basic Research, grant 97–01–00989.

DOI: https://doi.org/10.4213/dm400

Full text: PDF file (1957 kB)

English version:
Discrete Mathematics and Applications, 1999, 9:6, 563–581

Bibliographic databases:

UDC: 519.7
Received: 05.11.1998

Citation: S. S. Marchenkov, “On the expressibility of functions of many-valued logic in some logical-functional classes”, Diskr. Mat., 11:4 (1999), 110–126; Discrete Math. Appl., 9:6 (1999), 563–581

Citation in format AMSBIB
\Bibitem{Mar99}
\by S.~S.~Marchenkov
\paper On the expressibility of functions of many-valued logic in some logical-functional classes
\jour Diskr. Mat.
\yr 1999
\vol 11
\issue 4
\pages 110--126
\mathnet{http://mi.mathnet.ru/dm400}
\crossref{https://doi.org/10.4213/dm400}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1761017}
\zmath{https://zbmath.org/?q=an:0974.03028}
\transl
\jour Discrete Math. Appl.
\yr 1999
\vol 9
\issue 6
\pages 563--581


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Marchenkov, “Equational closure”, Discrete Math. Appl., 15:3 (2005), 289–298  mathnet  crossref  crossref  mathscinet  zmath  elib
    2. Marchenkov S.S., “The equational closure operator”, Doklady Mathematics, 72:3 (2005), 962–963  zmath  isi  elib
    3. S. S. Marchenkov, “On the structure of equationally closed classes”, Discrete Math. Appl., 16:6 (2006), 563–576  mathnet  crossref  crossref  mathscinet  zmath  elib
    4. S. S. Marchenkov, “A criterion for positive completeness in ternary logic”, J. Appl. Industr. Math., 1:4 (2007), 481–488  mathnet  crossref  mathscinet  zmath
    5. J. Appl. Industr. Math., 2:4 (2008), 542–549  mathnet  crossref  mathscinet  zmath
    6. Marchenkov, SS, “Strong closure operators on the set of partial Boolean functions”, Doklady Mathematics, 77:2 (2008), 288  crossref  mathscinet  zmath  isi  elib  scopus
    7. S. S. Marchenkov, “Positively closed classes of three-valued logic generated by one-place functions”, Discrete Math. Appl., 19:4 (2009), 375–382  mathnet  crossref  crossref  mathscinet  elib
    8. S. S. Marchenkov, “O zamknutykh klassakh funktsii $k$-znachnoi logiki, opredelyaemykh odnim endomorfizmom”, Diskretn. analiz i issled. oper., 16:6 (2009), 52–67  mathnet  mathscinet  zmath
    9. S. S. Marchenkov, “The closure operator in many-valued logic based on functional equations”, J. Appl. Industr. Math., 5:3 (2011), 383–390  mathnet  crossref  mathscinet  zmath
    10. S. S. Marchenkov, “O klassifikatsiyakh funktsii mnogoznachnoi logiki s pomoschyu grupp avtomorfizmov”, Diskretn. analiz i issled. oper., 18:4 (2011), 66–76  mathnet  mathscinet  zmath
    11. Marchenkov S.S., “Fe-klassifikatsiya funktsii mnogoznachnoi logiki”, Vestnik Moskovskogo universiteta. Seriya 15: Vychislitelnaya matematika i kibernetika, 2 (2011), 32–39  mathscinet  elib
    12. Marchenkov S.S., “Operator pozitivnogo zamykaniya”, Doklady Akademii nauk, 442:5 (2012), 598–598  crossref  mathscinet  zmath  isi  elib  scopus
    13. S. S. Marchenkov, “Atoms of the lattice of positively closed classes of three-valued logic”, Discrete Math. Appl., 22:2 (2012), 123–137  mathnet  crossref  crossref  mathscinet  elib
    14. S. S. Marchenkov, “Definition of positively closed classes by endomorphism semigroups”, Discrete Math. Appl., 22:5-6 (2012), 511–520  mathnet  crossref  crossref  mathscinet  elib
    15. S. S. Marchenkov, “Positive closed classes in the three-valued logic”, J. Appl. Industr. Math., 8:2 (2014), 256–266  mathnet  crossref  mathscinet  isi
    16. L. V. Ryabets, “Parametricheski zamknutye klassy giperfunktsii ranga 2”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 17 (2016), 46–61  mathnet
    17. S. S. Marchenkov, A. V. Chernyshev, “Basic positively closed classes in three-valued logic”, Discrete Math. Appl., 28:3 (2018), 157–165  mathnet  crossref  crossref  isi  elib
    18. S. S. Marchenkov, “Completeness criterion for the enumeration closure operator in three-valued logic”, Discrete Math. Appl., 30:1 (2020), 1–6  mathnet  crossref  crossref  mathscinet  isi  elib
    19. S. S. Marchenkov, “Extensions of the positive closure operator by using logical connectives”, J. Appl. Industr. Math., 12:4 (2018), 678–683  mathnet  crossref  crossref  elib
    20. V. I. Panteleev, L. V. Riabets, “The completeness criterion for closure operator with the equality predicate branching on the set of multioperations on two-element set”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 29 (2019), 68–85  mathnet  crossref
    21. S. S. Marchenkov, “O deistvii operatora implikativnogo zamykaniya na mnozhestve chastichnykh funktsii mnogoznachnoi logiki”, Diskret. matem., 32:1 (2020), 60–73  mathnet  crossref  mathscinet
    22. Vladimir I. Panteleyev, Leonid V. Riabets, “$E$-closed sets of hyperfunctions on two-element set”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 231–241  mathnet  crossref
    23. V. I. Panteleev, L. V. Riabets, “Classification of multioperations of rank $2$ by $E$-precomplete sets”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 34 (2020), 93–108  mathnet  crossref
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