why do we care about logic and proofs? » a computer science perspective
Computer scientists study how computers work. They research and analyze how computers take in raw data, store the data, process the data and then output the results. The goal is to figure out ways in which we as humans can use computer hardware and software to help us solve problems.
Creating these computer-based solutions may require us to write computer programs, develop algorithms and security protocols, or even create artificial intelligence. And, depending on the specific application of the solution and the significance of the impact that the solution may have on people's lives, we may also need to answer the question: how do we know for sure that the solution is correct? This is where a good foundation in logic and proofs comes in handy.
Logic is the science of correct reasoning or of drawing valid conclusions from premises or facts. It forms the basis of all mathematical and automated reasoning, and so computer scientists use the rules of logic to create automated solutions. The rules of logic help us make precise statements when constructing computer programs, and can also help us determine or prove whether or not a group of statements combined in an algorithm will always produce the correct output for all possible inputs. In general, we need proofs in order to confirm the total correctness of a computational solution. A proof tells us if our conclusion clearly follows from the premise or premises on which it is based.
Now, every computer scientist does not have to deal explicitly with proofs. But, if we want or need to verify the correctness of what we tell the computer to do, then we must be able to use the rules of logic to construct, or at least understand, proofs that show exactly how we arrived at a specific conclusion.
Sources:
C. Woodford. "Computers." explainthatstuff.com. https://www.explainthatstuff.com/howcomputerswork.html (accessed Sep. 12, 2022).
K. Arkoudas and Tech at Bloomberg. "The fundamental role of logic and proof in computer science." Bloomberg.com. https://www.bloomberg.com/company/stories/the-fundamental-role-of-logic-and-proof-in-computer-science/ (accessed Sep. 12, 2022).
K. Rosen, "The Foundations: Logic and Proofs," in Discrete Mathematics and Its Applications, 7th ed. New York, NY, USA: McGraw-Hill, 2012, ch. 1, pp. 1.
O. Levin, "Symbolic Logic and Proofs," in Discrete Mathematics: An Open Introduction, 3rd ed. Greeley, CO, USA: School of Mathematical Science University of Northern Colorado, 2021, ch. 3. [Online]. Available: http://discrete.openmathbooks.org/dmoi3/ch_logic.html.