For the academic conference LICS, see IEEE Symposium on Logic in Computer Science. Logic in computer science covers the overlap between the field of logic and that of computer science. Logic logic in computer science modelling and reasoning about systems pdf a fundamental role in computer science. 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. Gödel’s incompleteness theorem proves that any logical system powerful enough to characterize arithmetic will contain statements that can neither be proven true nor false 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. One of the first applications to use the term Artificial Intelligence was the Logic Theorist system developed by Allen Newell, J. Shaw, and Herbert Simon in 1956.
For example, If given a logical system that states “All humans are mortal” and “Socrates is human” a valid conclusion is “Socrates is mortal”. Of course this is a trivial example.
In actual logical systems the statements can be numerous and complex. It was realized early on that this kind of analysis could be significantly aided by the use of computers. The Logic Theorist validated the theoretical work of Bertrand Russell and Alfred North Whitehead in their influential work on mathematical logic called Principia Mathematica. In addition, subsequent systems have been utilized by logicians to validate and discover new logical theorems and proofs.
From the beginning of the field it was realized that technology to automate logical inferences could have great potential to solve problems and draw conclusions from facts. AI knowledge representation formalisms should be evaluated.
There is no more general or powerful known method for describing and analyzing information than FOL. The reason FOL itself is simply not used as a computer language is that it is actually too expressive, in the sense that FOL can easily express statements that no computer, no matter how powerful, could ever solve.
For this reason every form of knowledge representation is in some sense a trade off between expressivity and computability. The more expressive the language is, the closer it is to FOL, the more likely it is to be slower and prone to an infinite loop. For example, IF THEN rules used in Expert Systems are a very limited subset of FOL.