Thank you for your response,
“The logic used in computers however is not based on argument as you state.”
The logic used in computers are based on computability theory, modal logic and category theory. Mathematics of digital computers is Boolean Algebras and logic “1” and logic “0”/Binary System to construct logic circuits.
Wikipedia gives a fairly complete explanations of logic in computer science. Development of modal logic was started from Aristotle and Theophrastus. Then, C. I. Lewis founded modern modal logic in his 1910 Harvard thesis and in a series of scholarly articles beginning in 1912, etc. The mathematical structure of modal logic, namely Boolean Algebras.