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.
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 next step is to generate possible solutions and evaluate them.
Finally a solution is selected to be implemented and verified.
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. Shaw, as well as algorithmic methods, such as the resolution principle developed by John Alan Robinson.
Solving problems sometimes involves dealing with pragmatics, the way that context contributes to meaning, and semantics, the interpretation of the problem.
The ability to understand what the goal of the problem is, and what rules could be applied, represents the key to solving the problem.
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.