Analyzing the Role of Mathematical Logic in Information Technology

This report examines the critical role of mathematical logic within the field of information technology. The introduction establishes logic as the foundation of mathematical and automated reasoning, emphasizing its importance in defining mathematical statements and distinguishing between correct and incorrect reasoning. The report then delves into mathematical logic's applications, particularly in artificial intelligence, software validation, and computer programming, highlighting its utility in transforming specifications into code and ensuring program accuracy. It references articles discussing symbolic logic, its impact on engineering design, and its role in correcting errors. The report further discusses how mathematical logic is divided into subfields like model theory and recursion theory, crucial for problem-solving. Ultimately, the report concludes by summarizing the significant overlap between logic and IT, including the use of logic concepts in computer applications and the use of IT to aid logicians.

REPORT 1
Running head: REPORT
Discrete Mathematics
Mathematical Logic
JANUARY 12, 2020
STUDENT DETAILS

REPORT 2
Contents
Introduction.................................................................................................................................................3
Mathematical logic in Information technology –.........................................................................................3
Application of mathematical logic in information technology –..................................................................5
Conclusion...................................................................................................................................................6
References...................................................................................................................................................7

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Introduction
The logic is considered as the base of the mathematical reasoning along with automated
reasoning. It is stated by rule of logic there is specific meaning of the mathematical statement.
The rules of logic are helpful for the people to know reasons as well as attain data. The
mathematical logic is considered as sub-area of mathematic that discover application of
formal logics to arithmetic. There are three types of the mathematical logic. These types of
mathematical logic include model theory, set theory, and proof theory along with recursion
theory. The rule of logic gives exact definition along with purpose to mathematical statements.
The rules of logic is useful to make difference between improper as well as proper mathematical
reasoning. In addition to the significance of mathematical logic to know about mathematical
reasoning, it has certain applications in the information technology. It is differ from the design of
digital circuit to develop computer programming along with justification of accuracy of program.
The mathematical logic is helpful in sharing different outcomes on logic, mainly first order logic
along with definability. The report explains the relevance of mathematical logic in information
technology and application of mathematical logic in information technology is evaluated.
Mathematical logic in Information technology –
It is essential to know about the systematic mathematical logic (Dawkins and Cook, 2017). The
significance along with utilisation of mathematical logic in information technology can be
recognised by reviewing various articles.
1. Title : Introduction to Mathematical logic

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There is significant impact of the mathematical logic on the information technology. It is found
that there is the strong influence of mathematical logic on the area of AI (artificial intelligence).
From a starting of the field, it is analysed that the mathematical logic has great potential to
resolve various challenges as well as critical issues (Walicki, 2011). It is also helpful in
validating the accuracy of software specification. It is found that it is also used to transform the
provisions into effective and effectual code on diverse stages and to prove the equality between
application the measurement (De Swart, 2018).
2. Article: Mathematicians Measure Infinities and Find They’re Equal
It is stated in article ‘Mathematicians Measure Infinities and Find They’re Equal’ that the
mathematical logic is also known as symbolic logic. It is a formalized system of the deductive
logic. It is found that the mathematical logic employs the abstract signs for various components
of the natural language. In this way, the mathematical logic is helpful in analysing the different
declarations between sub-sets, sets and relationship in these rules of logic. It is helpful in
engineering design related to the machinery as well as construction. It also ensures the effective
operations as well as functions in the arithmetic and logic. It is stated by Hartnett (2017) that
there is connection between the size of infinity as well as difficulty of different theories of
mathematics.
3. Article: One hundred and two problems in mathematical logic
The article ‘One hundred and two problems in mathematical logic’ explains that the
mathematical logic is useful to correct the typographical errors as well as mistakes. It is reviewed

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that there is important place of the mathematical logic in information technology or computer
science. The mathematical logic divides the problems in different subdivisions. These
subdivisions are proof theory, model theory, intuitionism theory, set theory, as well as recursion
theory. These are based on subjective knowledge. It is found that it is significant in finding
correct results related to problem (Friedman, 2014).
Application of mathematical logic in information technology –
The mathematical logic is significantly used to discover the application of formal logics to
calculation as well as maths. The mathematical logic is fundamentally related to the information
technology. There are different aspects of the mathematical logic. These aspects of mathematical
logic are related to each other. It can see that these aspects are computability theory, category
logic along with constructive logic. They are helpful in enhancing the explanation and following
new term, idea along with notation (Hinman, 2018).
In addition, the computing theory is depended on concept described by logician along with
mathematician like Alan Turing and Alonzo Church. Alonzo first stated the presence of
algorithmically impenetrable issues utilising the concept of lambda definability. Alan provided
the primary compelling evaluation of what may be addressed the mechanical process. In
addition, Kurt Godel stated that the views of Turing are perfect (Post, 2016). Additionally, the
category theory is also helpful in presenting the view of mathematics that puts impact on relation
between different structures. It can say that this is tied to various facets of computer science,
such as type system for program language, the transition system theory, and model of program
language along with theory of programming language semantic. On the other hand, the model
theory is a research of classes of mathematical structure (such as group, field, graph, universe of

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set’s theory) from a viewpoint of mathematical logic. These theories are helpful in the better
application of information technology (Shoenfield, 2018).
Conclusion
In conclusion, it can say that the mathematical logic in the information technology covers the
overlap between area of logic and that of the information technology. It is sub-field of
mathematics. The mathematical logic is divided into three major fields, such as theoretical
foundation or evaluation, utilisation of information technology to help logician, as well as the
utilisation of concept from logic for computer application. In this way, it is helpful to resolve
problems related to arithmetic as well as logic.

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References
Dawkins, P.C. and Cook, J.P., (2017) Guiding reinvention of conventional tools of mathematical
logic: students’ reasoning about mathematical disjunctions. Educational Studies in
Mathematics, 94(3), pp.241-256.
De Swart, H., (2018) Philosophical and Mathematical Logic. USA: Springer International
Publishing.
Friedman, H. (2014) One hundred and two problems in mathematical logic. Available at:
https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/one-hundred-and-
two-problems-in-mathematical-logic/016CF7D4C4BD893879C471F40827BE39. [Access on
11/01/2020]
Hartnett, K. (2017) Mathematicians Measure Infinities and Find They’re Equal. Available at:
https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-
20170912/. [Access on 10/01/2020]
Hinman, P.G. (2018) Fundamentals of mathematical logic. USA: AK Peters/CRC Press.
Post, E.L., (2016) The Two-Valued Iterative Systems of Mathematical Logic.(AM-5) (Vol. 5).
UK: Princeton University Press.
Shoenfield, J.R. (2018) Mathematical logic. USA: CRC Press.
Walicki, M. (2011) Introduction to Mathematical Logic. Cambridge: Cambridge University
press