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Cardinality of the Set of Delta–Closed Classes of Functions of Multi–Valued Logic

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Abstract

A closure under composition operation and weak version of inversion operation is considered on the set of functions of k–valued logic. The cardinality of the set of all such closed classes is calculated.

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References

  1. S. V. Yabloriskii, Introduction to Discrete Mathematics (Vysshaya Shkola, Moscow, 2001) [in Russian].

    Google Scholar 

  2. D. Lau, Function Algebras on Finite Sets: A Basic Course on Many–Valued Logic and Clone Theory (Springer, Berlin, 2006).

    MATH  Google Scholar 

  3. E. L. Post, “Introduction to a General Theory of Elementary Propositions,” Amer. J. Math. 43 (3), 163 (1921).

    Article  MathSciNet  MATH  Google Scholar 

  4. E. L. Post, “The TWo–Valued Iterative Systems of Mathematical Logic,” Ann. Math. Stud. 5, 1941.

  5. Yu. I. Yanov and A. A. Muchnik, “Existence of k–Valued Closed Classes Having no Finite Basis,” Doklady Akad. Nauk SSSR 127 (1), 44 (1959).

    MathSciNet  MATH  Google Scholar 

  6. A. B. Ugol'nikov, “Some Problems Concerning Multi–Valued Logics,” in Proc, X Int. Workshop UDiscrete Mathematics and its Applications” (Moscow, MSU, February 16, 2010) Ed. by O. M. Kasirri–Zade (Moscow State Univ., Mech. Math. Faculty, Moscow, 2010), pp. 18–34.

    Google Scholar 

  7. D. E. Starodubtsev, “Classes of Functions of Multi–Valued Logic Closed with Respect to Superposition and Inversion Operations,” Vestn. Mosk. Univ., Matem. Mekhan., No. 2, 3 (2017).

    MathSciNet  MATH  Google Scholar 

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Correspondence to D.E. Starodubtsev.

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Original Russian Text © D.E. Starodubtsev, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 5, pp. 22–28.

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Starodubtsev, D. Cardinality of the Set of Delta–Closed Classes of Functions of Multi–Valued Logic. Moscow Univ. Math. Bull. 73, 190–195 (2018). https://doi.org/10.3103/S0027132218050042

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  • DOI: https://doi.org/10.3103/S0027132218050042

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