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Problem solving consists of using generic or ad hoc methods in an orderly manner to find solutions to problems.Some of the problem-solving techniques developed and used in philosophy, artificial intelligence, computer science, engineering, mathematics, or medicine are related to mental problem-solving techniques studied in psychology.
One such component is the emotional valence of "real-world" problems and it can either impede or aid problem-solving performance.
Researchers have focused on the role of emotions in problem solving , In conceptualization, human problem solving consists of two related processes: problem orientation and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills.
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.
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.
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.
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.