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However, already in 1958, John Mc Carthy proposed the advice taker, to represent information in formal logic and to derive answers to questions using automated theorem-proving.A important step in this direction was made by Cordell Green in 1969, using a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning.
It can also be applied to a product or process prior to an actual failure event—when a potential problem can be predicted and analyzed, and mitigation applied so the problem never occurs.
Techniques such as failure mode and effects analysis can be used to proactively reduce the likelihood of problems occurring.
Finally a solution is selected to be implemented and verified.
Problems have a goal to be reached and how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis.
Mental health professionals study the human problem solving processes using methods such as introspection, behaviorism, simulation, computer modeling, and experiment.
Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods.Researchers' underlying assumption was that simple tasks such as the Tower of Hanoi correspond to the main properties of "real world" problems and thus the characteristic cognitive processes within participants' attempts to solve simple problems are the same for "real world" problems too; simple problems were used for reasons of convenience and with the expectation that thought generalizations to more complex problems would become possible.Perhaps the best-known and most impressive example of this line of research is the work by Allen Newell and Herbert A. In computer science and in the part of artificial intelligence that deals with algorithms ("algorithmics"), problem solving includes techniques of algorithms, heuristics and root cause analysis.Much of computer science involves designing completely automatic systems that will later solve some specific problem -- systems to accept input data and, in a reasonable amount of time, calculate the correct response or a correct-enough approximation.In addition, people in computer science spend a surprisingly large amount of human time finding and fixing problems in their programs -- debugging.The ability to understand what the goal of the problem is, and what rules could be applied, represents the key to solving the problem.Sometimes the problem requires abstract thinking or coming up with a creative solution.The term problem solving means slightly different things depending on the discipline.For instance, it is a mental process in psychology and a computerized process in computer science.The use of computers to prove mathematical theorems using formal logic emerged as the field of automated theorem proving in the 1950s. Shaw, as well as algorithmic methods, such as the resolution principle developed by John Alan Robinson.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. In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science.