Editing Problem solving (section)

=== Logic ===
Formal [[logic]] concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution.

The use of computers to prove mathematical theorems using formal logic emerged as the field of [[automated theorem proving]] in the 1950s. It included the use of [[heuristic]] methods designed to simulate human problem solving, as in the [[Logic Theory Machine]], developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the [[Resolution (logic)|resolution]] principle developed by [[John Alan Robinson]].

In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for [[program verification]] in computer science. In 1958, [[John McCarthy (computer scientist)|John McCarthy]] proposed the [[advice taker]], to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by [[Cordell Green]] in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning.

The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, [[Robert Kowalski]] developed [[logic programming]] and [[SLD resolution]],<ref>{{cite journal|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf|title=Predicate Logic as a Programming Language|journal=Information Processing|volume=74|year=1974|access-date=2023-09-20|archive-date=2024-01-19|archive-url=https://web.archive.org/web/20240119025430/https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf|url-status=live}}</ref> which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving<ref>{{cite book|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf|title=Logic for Problem Solving|series=Artificial Intelligence Series|volume=7|publisher=Elsevier Science Publishing|year=1979|isbn=0-444-00368-1|access-date=2023-09-20|archive-date=2023-11-02|archive-url=https://web.archive.org/web/20231102032823/https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf|url-status=live}}</ref> and computational logic to improve human thinking.<ref>{{cite book|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf|title=Computational Logic and Human Thinking: How to be Artificially Intelligent|publisher=Cambridge University Press|year=2011|access-date=2023-09-20|archive-date=2024-06-01|archive-url=https://web.archive.org/web/20240601181910/https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf|url-status=live}}</ref>