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

Maydim A. Malkov

doi:doi:10.11648/j.pamj.20150404.16

| Peer-Reviewed

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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

Author Information

Maydim A. Malkov

Russian Research Center for Artificial Intelligence, Moscow, Russia

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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