*In response to criticism of his approach, emanating from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution, Problem solving is used when products or processes fail, so corrective action can be taken to prevent further failures.*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.Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods.

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.

In these disciplines, problem solving is part of a larger process that encompasses problem determination, de-duplication, analysis, diagnosis, repair, and other steps.

In addition, people in computer science spend a surprisingly large amount of human time finding and fixing problems in their programs -- debugging.

Formal logic is concerned with such issues as validity, truth, inference, argumentation and proof.

Interpersonal everyday problem solving is dependent upon the individual personal motivational and contextual components.

One such component is the emotional valence of "real-world" problems and it can either impede or aid problem-solving performance.The early experimental work of the Gestaltists in Germany placed the beginning of problem solving study (e.g., Karl Duncker in 1935 with his book The psychology of productive thinking The use of simple, novel tasks was due to the clearly defined optimal solutions and short time for solving, which made it possible for the researchers to trace participants' steps in problem-solving process.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.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.The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods.For instance, it is a mental process in psychology and a computerized process in computer science.There are two different types of problems, ill-defined and well-defined: different approaches are used for each.Other problem solving tools are linear and nonlinear programming, queuing systems, and simulation.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.Let's try θ = 30°: sin(−30°) = −0.5 and −sin(30°) = −0.5 So it is true for θ = 30° Let's try θ = 90°: sin(−90°) = −1 and −sin(90°) = −1 So it is also true for θ = 90° Is it true for all values of θ? Problem solving consists of using generic or ad hoc methods in an orderly manner to find solutions to problems.

## Comments How Do We Solve Problems

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