Logical Foundations of Computation: Techniques for Reliable and Efficient Programming
DOI:
https://doi.org/10.64137/31079458/IJCSEI-V2I1P101Keywords:
Mathematical logic, Programming paradigms, Program verification, Compiler design, Artificial intelligence, Database systemsAbstract
Mathematical logic forms the backbone of the field of computer science, providing precise reasoning about computational processes, program correctness, and designing system architecture. In computer programming, logical principles extend beyond theory and are actively applied as practical tools to improve program efficiency and reliability. Propositional as well as predicate logic serve as the building blocks for modeling data, algorithm verification, and understanding program behavior. Formal proof systems increase rigour in both software verification and compiler development. Programming paradigms like imperative, functional, and logic programming each incorporate logical principles in distinct ways, illustrating the flexibility of logic as a foundation for computation. Applications across different areas like compiler design, database systems, program verification, and artificial intelligence highlight the continuing relevance of logic in the modern computing landscape. Moreover, advances in automated reasoning, formal methods, and intelligent systems are expanding the impact of logic beyond its conventional boundaries. This paper explores the basic principles of mathematical logic, their role in various programming paradigms, and their wide-ranging applications in present-day computer science.
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