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

Maydim A. Malkov

doi:doi:10.11648/j.pamj.20150404.16

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

Maydim A. Malkov

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 4)

Received: 22 July 2015 Accepted: 3 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

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 4)
DOI	10.11648/j.pamj.20150404.16
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), 2015. 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.

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APA Style

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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  author = {Maydim A. Malkov},
  title = {Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic},
  journal = {Pure and Applied Mathematics Journal},
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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},
 year = {2015}
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Author Information

Maydim A. Malkov

Russian Research Center for Artificial Intelligence, Moscow, Russia

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APA Style

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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@article{10.11648/j.pamj.20150404.16,
  author = {Maydim A. Malkov},
  title = {Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {4},
  pages = {172-177},
  doi = {10.11648/j.pamj.20150404.16},
  url = {https://doi.org/10.11648/j.pamj.20150404.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150404.16},
  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},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic
AU  - Maydim A. Malkov
Y1  - 2015/08/12
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150404.16
DO  - 10.11648/j.pamj.20150404.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 172
EP  - 177
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150404.16
AB  - 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
VL  - 4
IS  - 4
ER  -

Copy | Download