Pure and Applied Mathematics Journal
Volume 4, Issue 4, August 2015, Pages: 172-177
Received: Jul. 22, 2015;
Accepted: Aug. 3, 2015;
Published: Aug. 12, 2015
Views 3755 Downloads 75
Maydim A. Malkov, Russian Research Center for Artificial Intelligence, Moscow, Russia
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
Maydim A. Malkov,
Post's thesis and wrong Janov-Mucnik's statement in multi-valued logic, Pure and Applied Mathematics Journal.
Vol. 4, No. 4,
2015, pp. 172-177.
E. L. Post, Introduction to a general theory of elementary propositions. Amer. J. Math. (1921) 43:4, 163-185.
Ju. I. Janov, A. A. Mucnik, On existence of k -valued closed classes without basis. Doklady SSSR (1959) 127:1, 44-46 (Russian).
D. Lau, Function algebras on finite sets, Springer, Berlin, 2006.
I. Rosenberg, Mal’cev algebras for universal algebra terms, Algebraic Logic and Universal Algebra in Computer Science, proceedings of conference (1988), 195-208.
A. I. Mal’cev, Iterative Post algebras, NGU, Novosibirsk, 1976 (in Russian).
M. A. Malkov, Algebra of logic and Post algebra (theory of two-valued functions), Mathematical Logic, Moscow, 2012 (in Russian).
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.
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.
Norman M. Martin, The Sheffer functions of 3-valued logic, J. of Symb. logic (1954) 19:1, 45-51.
M. A. Malkov, Classification of Boolean functions and their closed sets, Sop Transactions on Applied Math. (2014) 1:2, 172-193.
M. A. Malkov, Classification of closed sets of functions in multi-valued logic, Sop Transactions on Applied Math. (2014) 1:3, 96-105.