Algebra and Logic plays an important role in at least in some central areas of Digital transformation research, and it is algebra and logic that can be considered as the most important mechanisms in enabling strategic, fundamental advances in digital transformations of almost all sphears, which are provided and connected the social men life. The article presents the following results in an overview order:
Theorem about a level of logical expressivity;
Results, concerning the notion of a chaotic state of a system: Chaotic finite first order logic (determined by a finite free Boolean algebra) does not have synergistic effects; There does not exist a probabilistic model of a chaotic closed system in the form of a group.
REFERENCES
1.
N.
Serdyukova
and V.
Serdyukov
, Theory and Practice, Intelligent Systems Reference Library
(Springer Nature
, Switzerland
) 191
(2021
).2.
3.
N.
Serdyukova
and V.
Serdyukov
, Theory and Practice, Smart Innovation, Systems and Technologies
(Springer Nature
, Switzerland
) 91
(2018
).4.
B.
Mandelbrot
, The Fractal Geometry of Nature
(W.H. Freeman
, San Francisco
, 1983
).5.
I. R.
Shafarevich
, Basic Concepts of Algebra
(Izhevsk Republican Printing House
, Izhevsk
, 1999
).6.
7.
M.
Mesarovich
and Y.
Takahara
, General System Theory: Mathematical Foundations
(Academic Press
, New York
, 1975
).8.
D.
Gilbert
and V.
Ackerman
, Fundamentals of Theoretical Logic
(State Publishing House of Foreign Literature
, Moscow
, 1947
).9.
D. M.
Gabbay
, Labelled Deductive Systems
1
(Clarendon Press
, Oxford
, 1996
).10.
D. M.
Gabbay
, What Is a Logical System?
(Clarendon Press
, Oxford
, 1994
).11.
H.
Wansing
, Displaying Modal Logic
(Kluwer Academic Publishers
, Dordrecht
, 1998
).12.
N. K.
Vereshchagin
and A. V.
Shen
, Languages and Calculus, Lectures on Mathematical Logic and Theory of Algorithms. Part 2. Language and Calculus.
4 th ed. (Rev) (MCNMO
, Moscow
, 2012
).13.
G.
Gentzen
, Investigations of Logical Inferences, the Mathematical Theory of Logical Inference
(Moscow
, (1967
), pp. 9
–74
.14.
A.
Whitehead
and B.
Russell
, Principia Mathematica
(Cambridge University Press
, England
, 1910
–1913
).15.
P.
Halmos
and S.
Givant
, Logic as Algebra, Dolciani Mathematical Expositions
21
(The Mathematical Association of America
, Washington
, 1998
).16.
N. A.
Serdyukova
and V. I.
Serdyukov
, “Digitalization of Propositional Algebra and NPC
”, in Procedia Computer Science
(2019
).17.
N. A.
Serdyukova
and V. I.
Serdyukov
, Smart Education and e-Learning - Smart Pedagogy
305
, 456
–464
(2022
).18.
N. A.
Serdyukova
, V. I.
Serdyukov
, O. A.
Kusminova
, A. N.
Kusnetsov
and S. I.
Shishkina
, Smart Education and e-Learning - Smart Pedagogy
305
, 427
– 435
(2022
).19.
N. A.
Serdyukova
, V. I.
Serdyukov
and S. I.
Shishkina
, Smart Education and e-Learning - Smart Pedagogy
240
, 305
– 313
(2021
).20.
B.
Jónsson
and A.
Tarski
, American journal of mathematics
73
, 891
–939
(1951
); 74, 127–162 (1952).21.
22.
B. P.
Bezruchko
and D. A.
Smirnov
, Mathematical modeling and chaotic time series
(College
, Saratov
, 2005
).23.
24.
D. I.
Schlomiuk
, Transaction of the American Mathematical Society
149
(1970
).25.
26.
27.
C.
Massri
, F.
Holik
and A.
Plastino
, Math. Slovaca
69
(1
), 53
–70
(2019
).28.
V. G.
Durnev
and O.V.
Zetkina
, Methods of combinatorial group theory in modern cryptography
(YarSU
, Yaroslavl
, 2017
).29.
30.
31.
32.
M.
Verbitsky
and A.
Groups
, Lecture 1, Summer Mathematical School "Algebra and Geometry" (Yaroslavl)
.33.
C.
Atakan
, R. E.
Dagalp
, F.
Ozturk
, “Randomness and Chaos: Explorations of Chaos and Complexity
”, in Chaos, Complexity and Leadership
(2017
).
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