American Journal of Applied Science and Technology
36
https://theusajournals.com/index.php/ajast
VOLUME
Vol.05 Issue01 2025
PAGE NO.
36-38
10.37547/ajast/Volume05Issue02-10
The importance of mathematical logic schemes in
artificial intelligence
Zulfikharov Ilkhom Makhmudovich
Associate Professor of the Department of “Information Technologies” of Andijan State Technical Institute, Uzbekistan
Olimjonov Husanboy the son of Azamjon
Andijan State Technical Institute, 3rd year student, “Artificial Intelligence” program, Uzbekistan
Received:
21 December 2024;
Accepted:
23 January 2025;
Published:
25 February 2025
Abstract:
This аrticle аnаlyzes the impоrtаnce оf lоgic
circuits in аrtificiаl intelligence systems аnd their аpplicаtiоn
in vаriоus fields. Infоrmаtiоn is prоvided оn the principles оf оperаtiоn, structure аnd implementаtiоn stаges оf
lоgic circuits in аrtificiаl intelligence. Exаmples оf increаsing the efficiency оf lоgic circuits in аrtificiаl intelligence
systems аnd their аpplicаtiоn in reаl life аre given
.
Keywords:
Аrtificiаl intelligence, mаthemаtics, lоgic, reаsоning, lоgicаl schemа, аlgоrithms, mоdels, decisiоn tree,
Bаyesiаn netwоrk, Neurаl netwоrk, decisiоn mаking, prаcticаl exаmples
.
Introduction:
Decree of the President of the Republic
of Uzbekistan Sh. Mirziyoyev: “On additional measures
to improve the quality of education in higher education
institutions and ensure their active participation in
large-
scale reforms being implemented in the country”
No. PQ-
3775 dated June 5, 2018, “Measures to improve
the quality of education in mathematics and develop
scientific research in the field of mathema
tics” dated
May 7, 2020 The application of mathematical
considerations to artificial intelligence is of great
importance in the economic, social, and technical and
technological development of our country, in fulfilling
the tasks set forth in Resolutions No. PQ-4708 and No.
PQ-
4996 of February 17, 2021, “On measures to create
conditions for the accelerated introduction of artificial
intelligence technologies”. Mathematics provides the
foundation that allows artificial intelligence systems to
learn, reason, and make intelligent decisions.
Mathematics serves as the basis for artificial
intelligence algorithms and models, which allow
machines to process, analyze, and interpret large
amounts of data.
Artificial intelligence is the development and operation
of intelligent machines, drawing on many fields such as
psychology, mathematics, biology, and engineering to
create computers that can think based on new
information, react like humans, and change their
behavior.
The importance of mathematics in artificial intelligence
systems - algorithms use mathematical models and
calculations used in machine learning, so artificial
intelligence systems can automatically improve over
time based on feedback from the environment.
Artificial intelligence (AI) is actively used today in
various fields of science, technology, and everyday life.
The effectiveness of AI systems depends on their
decision-making ability, which is embodied in logical
schemes. Logical schemes play an important role in
various models of artificial intelligence, and their
correct operation ensures the reliability and efficiency
of AI systems.
METHODS
Mathematical logic is the laws, methods, and formulas
(forms) of reasoning, and its founder is considered to
be the ancient Greek thinker Aristotle (384-322 before
christ).
A mathematical statement is a statement that can only
accept one of two possible outcomes: “a certain event”
American Journal of Applied Science and Technology
37
https://theusajournals.com/index.php/ajast
American Journal of Applied Science and Technology (ISSN: 2771-2745)
or “an impossible (impossible) event”.
A logic diagram is a set of formal rules, logical
expressions, and algorithms used to solve a specific
problem or make a decision. It is used to control the
processes of processing, analyzing, and drawing
conclusions from information.
A number of scientists have conducted important
scientific research in the field of logical schemes (or
logical systems) in artificial intelligence. For example:
John McCarthy
–
Considered one of the founders of the
field of artificial intelligence, McCarthy has done
extensive research on logical schemes and formal
systems. His work “Programs with Common Sense”
(1959) explores the basic principles of logical reasoning
in artificial intelligence;
Alan Newell and Herbert Simon - together these
scientists developed a programming system called
“General Problem Solver” (1959), which learned to
solve problems using logical rules.
Jude Pearl -
his work “Probabilistic Reasoning in
Intelligent Systems” (1988) includes important
research on probabilistic reasoning and Bayesian
networks in artificial intelligence.
Raymond Reiter
–
Reiter provides detailed information
about default logic schemes and their applications in
artificial intelligence in his work “A Logic for Default
Reasoning” (1980).
Robert Kowalski - his work "Logic for Problem Solving"
(1979) provides important information on the use of
logic schemes in logic programming and artificial
intelligence.
These works have made a significant contribution to
the development of logic schemes in artificial
intelligence and are considered an important source for
researchers in the field.
RESULTS
Logic circuits are a key part of artificial intelligence, and
logic circuits used in AI systems accelerate and optimize
the decision-making process.
The use of various schemes - Bayesian networks in
probabilistic calculations, decision trees in data
classification, and neural networks in learning and
prediction - gives high results.
The effectiveness of artificial intelligence depends on
logic circuits, and properly designed logic circuits
ensure that systems make accurate and reliable
decisions.
Decision trees are one of the most widely used logic
diagrams in artificial intelligence and machine learning,
representing a visual and mathematical model for
analyzing data and making decisions.
Bayesian networks are logic circuits used in artificial
intelligence systems for decision-making under
uncertainty and probabilistic analysis. They represent
relationships between random variables in a graphical
form and operate on the basis of Bayes' rule.
Neural networks are a model used in artificial
intelligence systems to solve complex problems based
on logical circuits, based on the principle of processing
information, similar to the neurons of the human brain.
They play an important role in analyzing, learning, and
predicting large amounts of data.
Examples
. We present some practical examples from
various areas of artificial intelligence, including
processing data into logical circuits, decision-making,
and creating automated systems.
Example 1
. In medicine, AI-based diagnostic systems
use logic circuits to identify patients’ symptoms. For
example, if a patient has a high temperature, cough,
and difficulty breathing, the logic circuit considers the
possibility of COVID-19 or a lung infection and makes
recommendations to the doctor.
Example 2
. Autonomous cars make decisions based on
logic circuits. For example, if there is a red light ahead
(A=yes) and the car is moving (B=yes), then you should
apply the brakes (C=yes). This circuit helps to drive the
car safely.
Example 3
. If a client usually makes transactions not
exceeding 1 million soums, but suddenly a transaction
of 100 million soums is made, the system may block this
operation for verification or request additional
confirmation based on logical rules.
Example 4
. Logic circuits are used to respond to user
commands. If the user asks “How is the weather?”
(A=yes), then the system retrieves information from
the Internet and returns a response (B=yes).
Example 5
. Robots on a production line use logic
circuits to isolate defective products. For example, if a
product's size or weight is outside of the normal range,
logic decisions are made to destroy it or redirect it to a
rework line.
These examples demonstrate the importance of logic
circuits in artificial intelligence systems. They are one of
the main tools in ensuring the efficient and reliable
operation of AI.
DISCUSSION
Logical schemes used in artificial intelligence systems
are of fundamental importance in solving various
problems. Unlike traditional programming methods, AI
systems have the ability to learn and adapt to the
environment independently, and logical schemes play
an important role in this process.
American Journal of Applied Science and Technology
38
https://theusajournals.com/index.php/ajast
American Journal of Applied Science and Technology (ISSN: 2771-2745)
For example, Decision Trees and Bayesian Networks
can help you make decisions quickly and accurately.
Neural Networks can also automate complex data
processing and learning processes.
However, there are also problems associated with logic
circuits. In particular, improperly designed circuits can
lead to incorrect results, and computational complexity
can reduce the efficiency of the system. Therefore,
when developing logic circuits, special attention should
be paid to optimizing and correctly processing data.
CONCLUSION
Logical schemes are of great importance in the
development of artificial intelligence systems and
increasing their efficiency. They enable AI systems to
make accurate decisions, work quickly, and adapt. The
results show that logical schemes can be effectively
used in various AI areas, and their further improvement
is considered one of the promising directions.
Deep learning and optimization of logic circuits can
make a significant contribution to the future
development of artificial intelligence systems.
Therefore, it will be important to further expand
research in this area and develop new logic models in
the future.
This article serves as important theoretical and
practical information for specialists and researchers
working in the field of artificial intelligence.
REFERENCES
Зулфихaрoв И.М., Aкбaрoв С.A. Мaтемaтикaни
ўргaниш ҳaр бир кaсб эгaлaри хaёти учун муҳимдир
// “Педaгoгикa вa психoлoгиядa иннoвaциялaр”
jurnali 2-
мaхсус сoн
-
2020 й. 170
-
177 б. –Тoшкент.
Зулфихaрoв И.М. Тaлaбaлaрни мaтемaтикa фaнигa
қизиқтириш бизнинг бурчимиздир // “Физикa
-
мaтемaтикa фaнлaри” электрoн журнaл,
-
Тoшкент,
-
2020. 3-
сoн, 1
-
жилд,
-11-
16 б.
Зулфихaрoв И.М., Искaндaрoв Д.Х., Мaмaтoв Ф.У.
Тaлaбaлaрни
мaтемaтик
тaфaккурини
ривoжлaнтиришдa “интегрaл” қoнунигa aмaл
қилиш // “Differensial tenglamalar va matematikaning
turdosh
bo`limlari
zamonaviy
muammolari”
mavzusidagi Xalqaro ilmiy konferensiya, -Farg`ona, -
2020 yil. 12-13 mart, -308-
311 б.
Зулфихaрoв
И.М.
Мaтемaтикaдaн
aмaлий
мaшғулoтлaрдa
aхбoрoт
-
кoммуникaция
технoлoгиялaрининг ўрни // ЎзМУ ҳaбaрлaри, –
Тoшкент. 2018, –№ 1/1. –
118-
120 б.
Zulfixarov I.M. Matematik mantiqning diskret texnikaga
tatbiqlari
/
Andijon
mashinasozlik
instituti
“Mashinasozlik” ilmiy
-texnika jurnali 3-
son, № 3,
-2023
y.
Zulfixarov I.M., Mamasidiqov B.Q. Sun’iy intelektni
yaratishda bul algebrasining mantiqiy yo‘nalishdagi
matematik tahlili / Andijon mashinasozlik instituti
xalqaro ilmiy
–
texnik anjuman. -348-350 bet. 18-19-
sentabr, 2023-yil.
Zulfixarov I.M., Mamasidiqov B.Q. Mexatronika va
robototexnikada ikki karrali integralning mexanik
tatbiqlari / Andijon mashinasozlik instituti xalqaro
ilmiy-texnik anjuman. -2023 yil 19-21 oktyabr. 1027-
1030 bet.
Икрoмoв Х.Х. Oбзoр
существующих метoдoв
пoдгoтoвки рaзвития инфoрмaциoнных систем /
Нaмaнгaн МТИ мaхсус
-2023/5-
сoн.
Aтaжoнoвa С.Б. Interfaol ta’lim usullarining texnika
yo‘nalishlari talabalari faoliyatiga ta’siri / Нaмaнгaн
МТИ мaхсус
-2023/7-
сoн.
Zulfixarov I.M., No‘mon
ov A.SH., Norqulova M.SH.
Matematik mulohazalar bilan sun’iy intellektda bayes
tarmoqlarini tashkil etish. TATU Farg’ona filiali “Tadqiq
va tatbiq” ilmiy
-uslubiy jurnal SJIF 2024 (5.3). Tom 02.
Son. 02. 2024.
