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Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic

Received: 22 July 2015    Accepted: 03 August 2015    Published: 12 August 2015
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Abstract

Post stated that multi-valued logic has no principle difference with respect to two-valued logic. But Janov and Mucnik stated that multi-valued logic has essentially difference with respect to two-valued logic. We show that Post’s thesis is well but Janov-Mucnik’s statement is wrong

DOI 10.11648/j.pamj.20150404.16
Published in Pure and Applied Mathematics Journal (Volume 4, Issue 4, August 2015)
Page(s) 172-177
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Multi-Valued Logic, Post Algebra, Fictitious Closed Sets of Functions, Classification of Function

References
[1] E. L. Post, Introduction to a general theory of elementary propositions. Amer. J. Math. (1921) 43:4, 163-185.
[2] Ju. I. Janov, A. A. Mucnik, On existence of k -valued closed classes without basis. Doklady SSSR (1959) 127:1, 44-46 (Russian).
[3] D. Lau, Function algebras on finite sets, Springer, Berlin, 2006.
[4] I. Rosenberg, Mal’cev algebras for universal algebra terms, Algebraic Logic and Universal Algebra in Computer Science, proceedings of conference (1988), 195-208.
[5] A. I. Mal’cev, Iterative Post algebras, NGU, Novosibirsk, 1976 (in Russian).
[6] M. A. Malkov, Algebra of logic and Post algebra (theory of two-valued functions), Mathematical Logic, Moscow, 2012 (in Russian).
[7] M. A. Malkov, Complete generators in 3-valued logic and wrong Wheeler’s results, Int. J. of Math. and its Applications (2014) 2:4, 25-28.
[8] M. A. Malkov, Complete generators in 4-valued logic and Rousseau’s results, Int. J. of Math. and its Applications (2014) 2:4, 49-57.
[9] Norman M. Martin, The Sheffer functions of 3-valued logic, J. of Symb. logic (1954) 19:1, 45-51.
[10] M. A. Malkov, Classification of Boolean functions and their closed sets, Sop Transactions on Applied Math. (2014) 1:2, 172-193.
[11] M. A. Malkov, Classification of closed sets of functions in multi-valued logic, Sop Transactions on Applied Math. (2014) 1:3, 96-105.
Author Information
  • Russian Research Center for Artificial Intelligence, Moscow, Russia

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    Maydim A. Malkov. (2015). Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic. Pure and Applied Mathematics Journal, 4(4), 172-177. https://doi.org/10.11648/j.pamj.20150404.16

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    ACS Style

    Maydim A. Malkov. Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic. Pure Appl. Math. J. 2015, 4(4), 172-177. doi: 10.11648/j.pamj.20150404.16

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    AMA Style

    Maydim A. Malkov. Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic. Pure Appl Math J. 2015;4(4):172-177. doi: 10.11648/j.pamj.20150404.16

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      title = {Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic},
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      number = {4},
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      doi = {10.11648/j.pamj.20150404.16},
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      abstract = {Post stated that multi-valued logic has no principle difference with respect to two-valued logic. But Janov and Mucnik stated that multi-valued logic has essentially difference with respect to two-valued logic. We show that Post’s thesis is well but Janov-Mucnik’s statement is wrong},
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