Editing Logic in computer science (section)

== Logic applications for computers ==
There has always been a strong influence from mathematical logic on the field of [[artificial intelligence]] (AI). 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. [[Ronald J. Brachman|Ron Brachman]] has described [[first-order logic]] (FOL) as the metric by which all AI [[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 power (computer science)|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]]. A widely held belief maintains that 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.<ref>{{cite book|last=Levesque|first=Hector|title=Reading in Knowledge Representation|year=1985|publisher=Morgan Kaufmann|isbn=0-934613-01-X|page=[https://archive.org/details/readingsinknowle00brac/page/49 49]|author2=Ronald Brachman|editor=Ronald Brachman and Hector J. Levesque|chapter=A Fundamental Tradeoff in Knowledge Representation and Reasoning|quote=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.|chapter-url=https://archive.org/details/readingsinknowle00brac|url=https://archive.org/details/readingsinknowle00brac/page/49}}</ref> However, in a recent work<ref name=":0">{{Cite journal |last=Zhang |first=Heng |last2=Jiang |first2=Guifei |last3=Quan |first3=Donghui |date=2025-04-11 |title=A Theory of Formalisms for Representing Knowledge |url=https://ojs.aaai.org/index.php/AAAI/article/view/33674 |journal=Proceedings of the AAAI Conference on Artificial Intelligence |language=en |volume=39 |issue=14 |pages=15257–15264 |doi=10.1609/aaai.v39i14.33674 |issn=2374-3468|arxiv=2412.11855 }}</ref> by Heng Zhang et al., this belief has been rigorously challenged. Their findings establish that all universal knowledge representation formalisms are recursively isomorphic. Furthermore, their proof demonstrates that FOL can be translated into a pure procedural knowledge representation formalism defined by Turing machines with computationally feasible overhead, specifically within deterministic polynomial time or even at lower complexity.<ref name=":0" />

For example, IF–THEN rules used in [[expert system]]s 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 system]]s can support high-performance computation, especially if they take advantage of optimization algorithms and compilation.<ref>{{cite journal|last=Forgy|first=Charles|authorlink  = Charles Forgy|title=Rete: A Fast Algorithm for the Many Pattern/Many Object Pattern Match Problem*|journal=[[Artificial Intelligence (journal)|Artificial Intelligence]]|year=1982|volume=19|pages=17–37|url=http://web.yonsei.ac.kr/yusong/lecture/data/BI/Materials/1.1.Rete%20-%20A%20Fast%20Algorithm%20for%20the%20Many%20Pattern,%20Many%20Object%20Pattern%20Match%20Problem.pdf|access-date=25 December 2013|doi=10.1016/0004-3702(82)90020-0|archive-url=https://web.archive.org/web/20131227044049/http://web.yonsei.ac.kr/yusong/lecture/data/BI/Materials/1.1.Rete%20-%20A%20Fast%20Algorithm%20for%20the%20Many%20Pattern,%20Many%20Object%20Pattern%20Match%20Problem.pdf|archive-date=2013-12-27|url-status=dead}}</ref>

On the other hand, [[logic programming]], which combines the [[Horn clause]] subset of first-order logic with a [[non-monotonic logic|non-monotonic]] form of [[negation as failure|negation]], has both high expressive power and  efficient [[Implementation#Computer science|implementation]]s. In particular, the logic programming language [[Prolog]] is a  [[Turing completeness|Turing complete]] programming language. [[Datalog]] extends the [[relational database]] model with recursive relations, while [[answer set programming]] is a form of logic programming oriented towards difficult (primarily [[NP-hard]]) [[search problem]]s.

Another major area of research for logical theory is [[software engineering]]. Research projects such as the [[Knowledge Based Software Assistant]] and Programmer's Apprentice programs have applied logical theory to validate the correctness of [[software specification]]s. They have also used logical tools to transform the specifications into efficient code on diverse platforms and to prove the equivalence between the implementation and the specification.<ref>{{cite journal|last=Rich|first=Charles|author2=Richard C. Waters |title=The Programmer's Apprentice Project: A Research Overview|journal=IEEE Expert |date=November 1987|url=ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1004.pdf|archive-url=https://web.archive.org/web/20170706115702/ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1004.pdf|archive-date=2017-07-06|url-status=dead|access-date=26 December 2013}}</ref>  This formal transformation-driven approach is often far more effortful than traditional software development. However, in specific domains with appropriate formalisms and reusable templates the approach has proven viable for commercial products. The appropriate domains are usually those such as weapons systems, security systems, and real-time financial systems where failure of the system has excessively high human or financial cost. An example of such a domain is [[Very Large Scale Integration|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.<ref>{{cite book|last=Stavridou|first=Victoria|title=Formal Methods in Circuit Design|year=1993|publisher=Press Syndicate of the University of Cambridge|isbn=0-521-443369|url=https://books.google.com/books?id=Hf_AZfW2YWsC&q=VLSI+chip+design+formal+methods&pg=PA14|access-date=26 December 2013}}</ref>

Another important application of logic to computer technology has been in the area of [[frame language]]s and automatic classifiers. [[Frame language]]s such as [[KL-ONE]]  can be directly mapped to [[set theory]] and first-order logic. This allows specialized [[Theorem-prover|theorem prover]]s called classifiers to analyze the various declarations between [[set (mathematics)|set]]s, [[subset]]s, and [[relation (mathematics)|relation]]s 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]].<ref>{{cite journal|last=MacGregor|first=Robert|title=Using a description classifier to enhance knowledge representation|journal=IEEE Expert|date=June 1991|volume=6|issue=3|doi=10.1109/64.87683|pages=41–46|s2cid=29575443}}</ref><ref>{{cite journal|last=Berners-Lee |first=Tim |author2=James Hendler |author3=Ora Lassila |title=The Semantic Web A new form of Web content that is meaningful to computers will unleash a revolution of new possibilities |journal=[[Scientific American]] |date=May 17, 2001 |url=http://www.cs.umd.edu/~golbeck/LBSC690/SemanticWeb.html |author-link=Tim Berners-Lee |doi=10.1038/scientificamerican0501-34 |volume=284 |pages=34–43 |url-status=dead |archive-url=https://web.archive.org/web/20130424071228/http://www.cs.umd.edu/~golbeck/LBSC690/SemanticWeb.html |archive-date=April 24, 2013 |url-access=subscription }}</ref>

[[Temporal logic]] is used for reasoning in [[concurrency (computing)|concurrent systems]].<ref>{{cite conference | author = Colin Stirling | year = 1992 | title = Modal and Temporal Logics |pages=477–563| 
book-title = Handbook of Logic in Computer Science |editor1=S. Abramsky |editor-link1 = Samson Abramsky|editor2=D. M. Gabbay |editor-link2 = Dov Gabbay|editor3=T. S. E. Maibaum |editor-link3 = Tom Maibaum| volume = II| publisher = Oxford University Press | isbn = 0-19-853761-1 }}</ref>