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author: Mohamad Awwad


Urgency of the research. We consider crucial to distinguish between the original Boole’s logic and its modern development as Boolean logic in order to understand their theoretical and applied capacities. In addition, the development of Boolean logic constitutes a strong example about the relationships between logic, an algebraic language of thoughts, and computation.

Target setting. Boole’s logic is generally perceived as equivalent to Boolean logic despite their mathematical and conceptual differences. The influences of Boolean logic on computer science are recognized especially in their applications in circuits design. However, it appears that the influence of this logic on Cryptography is less cited in the literature when studying the relationships between logic and computer science.

Actual scientific researches and issues analysis. Studies of cryptographic Boolean functions and applications have been realized by scholars such as T. Cusick, and P. Stanica. Boolean methods in Mathematics are studied by Y. Crama and P. L. Hammer. Some differences between the original Boole’s logic and the modern Boolean logic have been pointed out and promoted by N. J. Wildberger. Boole’s algebra as a mathematical language of thought has been presented in many fundamental handbooks such as those written or edited by D. M. Gabbay, J. Woods, W. Kneale, M. Kneale, and L. Haaparanta.

The research objective. The first objective of this research is to formally explain the theoretical differences between Boole’s logic and the modern Boolean logic. The second objective is to show the immense role of Boolean logic in computer science through the developments of circuits design and cryptography.

The statement of basic material. The developments of an algebraic logical language of thoughts by G. Boole are considered using historical and theoretical perspectives. The technical implementations of Boolean logic in combinational circuits and in modern cryptography show strong influences of a 19th century logic on the latest technologies of computing.

Conclusions. In this research we came to the following results: 1) Boolean logic is different but derived from the original logic of Boole; it has been obtained due to a transformational process that led to a two-valued logic. 2) This two-valued logic made possible its digital implementation into a binary system. 3) The use of Boolean logic in circuits’ analysis and design constitutes a strong example of the influences of logic on computer science. 4) The use of Boolean logic in cryptography constitutes another strong example of the role of logic in modern computation.

Keywords: Logic, Computer Science, Boole’s Algebra of logic, Boolean Logic, Circuit analysis and Design, Cryptography, Error Correcting Code.


References:

1. Cusick, TW & Stanica, P 2017. Cryptographic Boolean functions and applications, Academic Press.

2. Crama, Y & Hammer, PL 2010. Boolean models and methods in mathematics, computer science, and engineering, Cambridge University Press, Vol. 2.

3. Kneale, W & Kneale, M 1962. The development of logic, Oxford University Press.

4. Boole, G 1957. The laws of thought, Dover, New York (original edition 1854).

5. Boole, R 1947. The Mathematical Analysis of Logic, Philosophical library.

6. Shannon, CE 1938. A symbolic analysis of relay and switching circuits, Electr. Eng. Vol. 57, № 12. P. 713–723.

7. Foundations of Computer Science/Computing Machinery 2017. Wikibooks, open books for an open world. Available from: <https://en.wikibooks.org/wiki/Foundations_of_Computer_Science/Computing_Machinery> [05 May 2021].