Problem solving is studied everywhere from Tower of Hanoi to theorem provers
Getting across town and debugging a program are both problem solving, one simple and one complex. Psychologists, computer scientists, engineers and military planners all study how obstacles are overcome, and they keep rediscovering one powerful trick: split a big problem into smaller pieces, a principle called decomposition.
Researchers sort problems several ways. Well-defined ones have clear goals and expected answers, allowing plenty of upfront planning, while ill-defined ones leave it unclear what a good outcome even looks like. Some problems are formal and fact-based; others are socio-emotional, like choosing a gift or behaving tactfully. Common mental traps include confirmation bias, mental set and functional fixedness, the tendency to see an object only in its usual role.
Early experimental work came from German Gestalt psychologists such as Karl Duncker, whose The Psychology of Productive Thinking appeared in 1935, and later from Allen Newell and Herbert A. Simon. In the 1960s and early 1970s participants tackled unfamiliar but tidy puzzles such as the Tower of Hanoi, whose optimal solutions could be found quickly, letting researchers watch the whole process. Studies also show that poor emotional control can derail focus and leave people fatigued or stuck.
Computers joined in during the 1950s through automated theorem proving. Newell, Simon and J. C. Shaw built the Logic Theory Machine to imitate human heuristics, while John Alan Robinson's resolution principle took a purely algorithmic route. John McCarthy proposed his advice taker in 1958, and in 1969 Cordell Green applied a resolution prover to question answering and robot planning. Critics at MIT noted it looked nothing like human reasoning, prompting Robert Kowalski to develop logic programming, which works by decomposition.
Engineers use diagnosis to explain failures after the fact and methods like failure mode and effects analysis to anticipate them. In Peirce's logical scheme, abduction proposes hypotheses, deduction refines them and induction tests them with data. The ACT-R model of cognition pictures the mind handling a stack of goals and subgoals, working on one task at a time.
Source: Problem solving
