Logic in computer science

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For the academic conference LICS, see Symposium on Logic in Computer Science.
logic gates

Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas:

  • Theoretical foundations and analysis
  • Use of computer technology to aid logicians
  • Use of concepts from logic for computer applications

Theoretical foundations and analysis

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.[1][2] 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."[3]. In addition some other major areas of theoretical overlap between logic and computer science are:

Computers to assist logicians

One of the first applications to use the term artificial intelligence was the Logic Theorist system developed by Allen Newell, Cliff Shaw, and Herbert Simon in 1956. One of the things that a logician does is to take a set of statements in logic and deduce the conclusions (additional statements) that must be true by the laws of logic. For example, if given the statements "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. 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 mathematical theorems and proofs.[7]

Logic applications for computers

There has always been a strong influence from mathematical logic on the field of

knowledge representation formalisms should be evaluated. First-order logic is a general and powerful method for describing and analyzing information. 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.[8]

For example, IF–THEN rules used in expert systems approximate to a very limited subset of FOL. Rather than arbitrary formulas with the full range of logical operators the starting point is simply what logicians refer to as modus ponens. As a result, rule-based systems can support high-performance computation, especially if they take advantage of optimization algorithms and compilation.[9]

On the other hand,

NP-hard) search problems
.

Another major area of research for logical theory is

Very Large Scale Integrated (VLSI) design—the process for designing the chips used for the CPUs and other critical components of digital devices. An error in a chip can be catastrophic. Unlike software, chips can't be patched or updated. As a result, there is commercial justification for using formal methods to prove that the implementation corresponds to the specification.[11]

Another important application of logic to computer technology has been in the area of

theorem provers called classifiers to analyze the various declarations between sets, subsets, and relations in a given model. In this way the model can be validated and any inconsistent definitions flagged. The classifier can also infer new information, for example define new sets based on existing information and change the definition of existing sets based on new data. The level of flexibility is ideal for handling the ever changing world of the Internet. Classifier technology is built on top of languages such as the Web Ontology Language to allow a logical semantic level on top of the existing Internet. This layer is called the Semantic Web.[12][13]

concurrent systems.[14]

See also

References

  1. ^ Lewis, Harry R. (1981). Elements of the Theory of Computation. Prentice Hall.
  2. ISBN 9783211826379
    . Retrieved 26 December 2013.
  3. ISBN 9781107002661
    . Retrieved 17 August 2015.
  4. ISBN 978-0465026562
    .
  5. ^ McCarthy, John; P.J. Hayes (1969). "Some philosophical problems from the standpoint of artificial intelligence" (PDF). Machine Intelligence. 4: 463–502.
  6. ^ Barr, Michael; Charles Wells (1998). Category Theory for Computing Science (PDF). Centre de Recherches Mathématiques.
  7. ISBN 978-0262560924
    .
  8. ISBN 0-934613-01-X
    . The good news in reducing KR service to theorem proving is that we now have a very clear, very specific notion of what the KR system should do; the bad new is that it is also clear that the services can not be provided... deciding whether or not a sentence in FOL is a theorem... is unsolvable.
  9. doi:10.1016/0004-3702(82)90020-0. Archived from the original
    (PDF) on 2013-12-27. Retrieved 25 December 2013.
  10. ^ Rich, Charles; Richard C. Waters (November 1987). "The Programmer's Apprentice Project: A Research Overview" (PDF). IEEE Expert. Archived from the original (PDF) on 2017-07-06. Retrieved 26 December 2013.
  11. ISBN 0-521-443369
    . Retrieved 26 December 2013.
  12. S2CID 29575443
    .
  13. doi:10.1038/scientificamerican0501-34. Archived from the original
    on April 24, 2013.
  14. ISBN 0-19-853761-1
    .

Further reading

External links
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