Logic in Computer Science

Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing.  Church first showed the existence of algorithmically unsolvable problems using his notion of lambda-definability. Turing gave the first compelling analysis of what can be called a mechanical procedure and Kurt Gödel asserted that he found Turing's analysis "perfect." In addition some other major areas of theoretical overlap between logic and computer science are:

• Gödel's incompleteness theorem proves that any logical system powerful enough to characterize arithmetic will contain statements that can neither be proved nor disproved within that system. This has direct application to theoretical issues relating to the feasibility of proving the completeness and correctness of software.
• The frame problem is a basic problem that must be overcome when using first-order logic to represent the goals and state of an artificial intelligence agent.
• The Curry-Howard correspondence is a relation between logical systems and software. This theory established a precise correspondence between proofs and programs. In particular it showed that terms in the simply-typed lambda-calculus correspond to proofs of intuitionistic propositional logic.
• Category theory represents a view of mathematics that emphasizes the relations between structures. It is intimately tied to many aspects of computer science: type systems for programming languages, the theory of transition systems, models of programming languages and the theory of programming language semantics.

Courtesy of Wikipedia

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