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Rehabilitation psychologists studying individuals with frontal lobe injuries have found that deficits in emotional control and reasoning can be remediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems.
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.
Well-defined problems allow for more initial planning than ill-defined problems.
Solving problems sometimes involves dealing with pragmatics, the way that context contributes to meaning, and semantics, the interpretation of the problem.
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.
In these disciplines, problem solving is part of a larger process that encompasses problem determination, de-duplication, analysis, diagnosis, repair, and other steps.
Other problem solving tools are linear and nonlinear programming, queuing systems, and simulation.
Formal logic is concerned with such issues as 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.