Natural deduction for Yuriev's logic
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 1, pp. 46-52.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we consider the three-valued Yuriev's logic constructed for the simulating of the work of a biological neuron and an artificial neural networks. We formulate a natural deduction system which is adequate with respect to the semantics of the considered logic.
Keywords: natural deduction, three-valued logic, Yuriev's logic, logic of neuron network, logic of biological neuron.
@article{CHFMJ_2017_2_1_a4,
     author = {Ya. I. Petrukhin},
     title = {Natural deduction for {Yuriev's} logic},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {46--52},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a4/}
}
TY  - JOUR
AU  - Ya. I. Petrukhin
TI  - Natural deduction for Yuriev's logic
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2017
SP  - 46
EP  - 52
VL  - 2
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a4/
LA  - ru
ID  - CHFMJ_2017_2_1_a4
ER  - 
%0 Journal Article
%A Ya. I. Petrukhin
%T Natural deduction for Yuriev's logic
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2017
%P 46-52
%V 2
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a4/
%G ru
%F CHFMJ_2017_2_1_a4
Ya. I. Petrukhin. Natural deduction for Yuriev's logic. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 1, pp. 46-52. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a4/

[1] D.N. Yuriev, “New three-valued logic”, Proceedings of the research logical seminar of Institute of philosophy of Russian Academy of Sciences, 15, 2001, 120–125 (In Russ.) | Zbl

[2] A.S. Karpenko, “Nonregularity and ‘`essential" nonmonotonicity of Yuriev’s logic Y$_{3}$”, Proceedings of the research logical seminar of Institute of philosophy of Russian Academy of Sciences, 16, 2002, 54–58 (In Russ.) | Zbl

[3] S. C. Kleene, “On a notation for ordinal numbers”, J. of Symbolic Logic, 3:4 (1938), 150–155 | DOI | MR

[4] S. C. Kleene, Introduction to metamathematics, D. Van Nostrand Company, Inc., New York, Toronto, 1952, x + 550 pp. | MR | MR

[5] A.S. Karpenko, “Non truth-functional Kleene's logic with antiboolean operation”, Proceedings of the research logical seminar of Institute of philosophy of Russian Academy of Sciences, 15, 2001, 41–45 (In Russ.) | Zbl

[6] S.V. Yablonskiy, “Functional constructions in $k$-valued logic”, Proceedings of the Steklov Institute of Mathematics, 51, 1958, 5–142 (In Russ.)

[7] E. Post, “Introduction to a general theory of elementary propositions”, American J. of Mathematics, 43:3 (1921), 163–185 | DOI | MR | Zbl

[8] N. Ressher, Many-valued logic, McGraw Hill, N. Y., 1959, xv+359 pp.

[9] L. Henkin, “The completeness of the first-order functional calculus”, J. of Symbolic Logic, 14:3 (1949), 159–166 | DOI | MR | Zbl

[10] A. Tamminga, “Correspondence analysis for strong three-valued logic”, Logical Investigations, 2014, no. 20, 255–268 | MR | Zbl