Editing Problem solving (section)

== Definition ==
The term ''problem solving'' has a slightly different meaning depending on the discipline. 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. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems.<ref name=":0">{{cite book|author-link1=Daniel Schacter|last1=Schacter|first1=D.L.|last2=Gilbert|first2= D.T.|last3=Wegner|first3=D.M.|title=Psychology|edition=2nd|location=New York|year=2011|publisher= Worth Publishers|page=376}}</ref> 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 end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires [[abstract thinking]] or coming up with a creative solution.

Problem solving has two major domains: [[Mathematical problem|mathematical problem solving]] and personal problem solving. Each concerns some difficulty or barrier that is encountered.<ref name="Zimmermann">{{cite conference |first=Bernd |last=Zimmermann |year=2004 |title=On mathematical problem-solving processes and history of mathematics |url=https://www.researchgate.net/publication/238733375 |conference=ICME 10|location=Copenhagen}}</ref>

=== Psychology ===
Problem solving in psychology refers to the process of finding solutions to problems encountered in life.<ref>{{cite book|first=Donald K.|last=Granvold|chapter=Cognitive-Behavioral Therapy with Adults|editor-first=Jerrold R.|editor-last=Brandell|title=Theory and Practice in Clinical Social Work|year=1997|publisher=Simon and Schuster|isbn=978-0-684-82765-0|pages=[https://books.google.com/books?id=K9Hm0UuFGJ0C&pg=PA189 189]}}</ref> Solutions to these problems are usually situation- or context-specific. The process starts with [[problem finding]] and [[problem shaping]], in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an ''end goal'' to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis.<ref>{{cite book|chapter=Introduction to the study of problem solving|title=Problem Solving|first=S. Ian|last=Robertson|publisher=Psychology Press|year=2001|isbn=0-415-20300-7}}</ref>

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.<ref>{{cite journal | last1 = Rubin | first1 = M. | last2 = Watt | first2 = S. E. | last3 = Ramelli | first3 = M. | year = 2012 | title = Immigrants' social integration as a function of approach-avoidance orientation and problem-solving style | journal = International Journal of Intercultural Relations | volume = 36 | issue = 4| pages = 498–505 | doi = 10.1016/j.ijintrel.2011.12.009 | hdl = 1959.13/931119 | hdl-access = free }}</ref> Problem solving has been defined as a higher-order [[cognitive]] process and [[intelligence|intellectual function]] that requires the modulation and control of more routine or fundamental skills.<ref name="G&L87">{{cite book | author1= Goldstein F. C. |author2=Levin H. S. |year=1987 |chapter=Disorders of reasoning and problem-solving ability |editor1=M. Meier |editor2=A. Benton |editor3=L. Diller |title=Neuropsychological rehabilitation |place=London |publisher=Taylor & Francis Group.}}</ref>

Empirical research shows many different strategies and factors influence everyday problem solving.<ref>{{multiref2
|1={{cite book |last1=Vallacher |first1=Robin |last2=M. Wegner |first2=Daniel |chapter=Action Identification Theory |title=Handbook of Theories of Social Psychology |pages=327–348 |doi=10.4135/9781446249215.n17|year=2012 |isbn=978-0-85702-960-7 }}
|2={{cite journal | doi = 10.1080/01650250143000319 | volume=26 | issue=1 | title=Gender differences in older adults' everyday cognitive collaboration | journal=International Journal of Behavioral Development | pages=45–59| pmc=2909137 |pmid=20657668| year=2002 | last1=Margrett | first1=J. A | last2=Marsiske | first2=M }}
|3={{cite journal | doi = 10.1093/geront/gnt118 | pmid=24142914 | volume=54 | issue=1 | title=The Convoy Model: Explaining Social Relations From a Multidisciplinary Perspective | journal=The Gerontologist | pages=82–92| pmc=3894851 | year=2013 | last1=Antonucci | first1=T. C | last2=Ajrouch | first2=K. J | last3=Birditt | first3=K. S }}
}}</ref> [[Rehabilitation psychology|Rehabilitation psychologists]] studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems.<ref name="Rath2003">{{cite journal |last1=Rath |first1=Joseph F. |last2=Simon |first2=Dvorah |last3=Langenbahn |first3=Donna M. |last4=Sherr |first4=Rose Lynn |last5=Diller |first5=Leonard |title=Group treatment of problem-solving deficits in outpatients with traumatic brain injury: A randomised outcome study |journal=Neuropsychological Rehabilitation |year= 2003 |volume=13 |issue=4 |pages=461–488 |doi=10.1080/09602010343000039 |s2cid=143165070 |url=https://www.researchgate.net/publication/247514323}}</ref> Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the [[Valence (psychology)|emotional valence]] of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving,<ref name=DZurilla>{{multiref2
|1={{cite journal | last1 = D'Zurilla | first1 = T. J. | last2 = Goldfried | first2 = M. R. | year=1971 | title = Problem solving and behavior modification | journal = Journal of Abnormal Psychology | volume = 78 | issue = 1| pages = 107–126 | doi=10.1037/h0031360 | pmid = 4938262 |ref=Reference-DZurilla1971}}
|2={{cite book |author1= D'Zurilla, T. J. |author2=Nezu, A. M. |year=1982 |chapter=Social problem solving in adults |editor=P. C. Kendall  |title=Advances in cognitive-behavioral research and therapy |volume=1 |pages=201–274 |place=New York |publisher=Academic Press}}
}}</ref> demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia.<ref name="rath2004">{{cite journal |last1=Rath |first1=J. F. |last2=Langenbahn |first2=D. M. |last3=Simon |first3=D |last4=Sherr |first4=R. L. |last5=Fletcher |first5=J. |last6=Diller |first6=L. |year=2004 |title=The construct of problem solving in higher level neuropsychological assessment and rehabilitation*1 |journal=Archives of Clinical Neuropsychology |volume=19 |issue=5 |pages=613–635 |doi=10.1016/j.acn.2003.08.006 |pmid=15271407 |doi-access=free}}</ref> {{clarify|text=In conceptualization, |date=September 2023}}human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills.<ref>{{Cite journal|last1=Rath|first1=Joseph F.|last2=Hradil|first2=Amy L.|last3=Litke|first3=David R.|last4=Diller|first4=Leonard|date=2011|title=Clinical applications of problem-solving research in neuropsychological rehabilitation: Addressing the subjective experience of cognitive deficits in outpatients with acquired brain injury.|journal=Rehabilitation Psychology|language=en|volume=56|issue=4|pages=320–328|doi=10.1037/a0025817|pmid=22121939|pmc=9728040 |issn=1939-1544}}</ref> People's strategies cohere with their goals<ref>{{cite journal |last1=Hoppmann |first1=Christiane A. |last2=Blanchard-Fields |first2=Fredda |author-link2=Fredda Blanchard-Fields |title=Goals and everyday problem solving: Manipulating goal preferences in young and older adults |journal=Developmental Psychology |year= 2010 |volume=46 |issue=6 |pages=1433–1443 |doi=10.1037/a0020676|pmid=20873926 }}</ref> and stem from the process of comparing oneself with others.

=== Cognitive sciences ===
Among the first experimental psychologists to study problem solving were the [[Gestalt psychology|Gestaltists]] in [[Germany]], such as [[Karl Duncker]] in ''The Psychology of Productive Thinking'' (1935).<ref name=Duncker>{{cite book | last= Duncker|first=Karl |year=1935 |title=Zur Psychologie des produktiven Denkens |trans-title=The psychology of productive thinking |location=Berlin |publisher=Julius Springer |language=de}}</ref> Perhaps best known is the work of [[Allen Newell]] and [[Herbert A. Simon]].<ref name="Newell">{{cite book |last1=Newell|first1= Allen |last2=Simon|first2= Herbert A. |year=1972 |title=Human problem solving |location=Englewood Cliffs, N.J. |publisher=Prentice-Hall}}</ref>

Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks.<ref>For example:
* X-ray problem, by {{cite book | last= Duncker|first= Karl |year=1935 |title=Zur Psychologie des produktiven Denkens |trans-title=The psychology of productive thinking |place=Berlin |publisher=Julius Springer |language=de}}
* Disk problem, later known as [[Tower of Hanoi]], by {{cite journal | last1=Ewert | first1=P. H. | last2=Lambert | first2=J. F. | title=Part II: The Effect of Verbal Instructions upon the Formation of a Concept | journal=The Journal of General Psychology | publisher=Informa UK Limited | volume=6 | issue=2 | year=1932 | issn=0022-1309 | doi=10.1080/00221309.1932.9711880 | pages=400–413 | url=https://www.tandfonline.com/doi/abs/10.1080/00221309.1932.9711880 | url-access=subscription | access-date=2019-06-09 | archive-date=2020-08-06 | archive-url=https://web.archive.org/web/20200806135752/https://www.tandfonline.com/doi/abs/10.1080/00221309.1932.9711880 | url-status=live }}</ref><ref>{{cite book | last= Mayer|first= R. E. |year=1992 |title=Thinking, problem solving, cognition |edition=Second |location=New York |publisher=W. H. Freeman and Company}}</ref> These simple problems, such as the [[Tower of Hanoi]], admitted [[optimal solution]]s that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic [[cognitive process]]es by which more complex "real world" problems are solved.

An outstanding problem-solving technique found by this research is the principle of [[Decomposition (computer science)|decomposition]].<ref>{{cite journal |first1=J. Scott|last1=Armstrong|first2=William B. Jr.|last2=Denniston|first3=Matt M.|last3=Gordon |year=1975|title=The Use of the Decomposition Principle in Making Judgments |url=http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/DecompositionPrinciple.pdf  |journal=Organizational Behavior and Human Performance |volume=14 |issue=2 |pages=257–263 |doi=10.1016/0030-5073(75)90028-8 |archive-url=https://web.archive.org/web/20100620221713/http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/DecompositionPrinciple.pdf |archive-date=2010-06-20 |s2cid=122659209}}</ref>

=== Computer science ===

{{Expand section|date=September 2018}}

Much of computer science and [[artificial intelligence]] involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. [[Algorithm]]s are recipes or instructions that direct such systems, written into [[computer program]]s.

Steps for designing such systems include problem determination, [[heuristic]]s, [[root cause analysis]], [[Data deduplication|de-duplication]], analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, [[queuing systems]], and simulation.<ref name="MalakootiMCDM">{{cite book |last1=Malakooti |first1=Behnam |title=Operations and Production Systems with Multiple Objectives |year=2013 |publisher=John Wiley & Sons |isbn=978-1-118-58537-5}}</ref> A large, perennial obstacle is to find and fix errors in computer programs: [[debugging]].

=== Logic ===
Formal [[logic]] concerns issues like 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. 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. Simon and J. C. Shaw, as well as algorithmic methods such as the [[Resolution (logic)|resolution]] principle developed by [[John Alan Robinson]].

In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for [[program verification]] in computer science. In 1958, [[John McCarthy (computer scientist)|John McCarthy]] proposed the [[advice taker]], to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by [[Cordell Green]] in 1969, who used 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. In response to criticism of that approach from researchers at MIT, [[Robert Kowalski]] developed [[logic programming]] and [[SLD resolution]],<ref>{{cite journal|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf|title=Predicate Logic as a Programming Language|journal=Information Processing|volume=74|year=1974|access-date=2023-09-20|archive-date=2024-01-19|archive-url=https://web.archive.org/web/20240119025430/https://www.doc.ic.ac.uk/~rak/papers/IFIP%2074.pdf|url-status=live}}</ref> which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving<ref>{{cite book|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf|title=Logic for Problem Solving|series=Artificial Intelligence Series|volume=7|publisher=Elsevier Science Publishing|year=1979|isbn=0-444-00368-1|access-date=2023-09-20|archive-date=2023-11-02|archive-url=https://web.archive.org/web/20231102032823/https://www.doc.ic.ac.uk/~rak/papers/LogicForProblemSolving.pdf|url-status=live}}</ref> and computational logic to improve human thinking.<ref>{{cite book|last=Kowalski|first=Robert|url=https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf|title=Computational Logic and Human Thinking: How to be Artificially Intelligent|publisher=Cambridge University Press|year=2011|access-date=2023-09-20|archive-date=2024-06-01|archive-url=https://web.archive.org/web/20240601181910/https://www.doc.ic.ac.uk/~rak/papers/newbook.pdf|url-status=live}}</ref>

=== Engineering ===
When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further [[failure]]s. Such techniques can also be applied to a product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as [[failure mode and effects analysis]] can proactively reduce the likelihood of problems.

In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, [[Abductive reasoning|abduction]] generates new ideas or hypotheses (asking "how?"); [[Deductive reasoning|deduction]] evaluates and refines hypotheses based on other plausible premises (asking "why?"); and [[Inductive reasoning|induction]] justifies a hypothesis with empirical data (asking "how much?").<ref name="Staat">{{cite journal|last=Staat|first=Wim|title=On abduction, deduction, induction and the categories|journal=Transactions of the Charles S. Peirce Society|volume=29|number=2|year=1993|pages=225–237}}</ref> The objective of abduction is to determine which hypothesis or proposition to test, not which one to adopt or assert.<ref name="Sullivan">{{cite journal|last=Sullivan|first=Patrick F.|title=On Falsificationist Interpretations of Peirce|journal=Transactions of the Charles S. Peirce Society|volume=27|number=2|year=1991|pages=197–219}}</ref> In the [[Charles S. Peirce|Peircean]] logical system, the logic of abduction and deduction contribute to our conceptual understanding of a phenomenon, while the logic of induction adds quantitative details (empirical substantiation) to our conceptual knowledge.<ref name="Yu">{{cite conference|last=Ho|first=Yu Chong|title=Abduction? Deduction? Induction? Is There a Logic of Exploratory Data Analysis?|year=1994|conference=Annual Meeting of the American Educational Research Association|location=New Orleans, La.|url=https://files.eric.ed.gov/fulltext/ED376173.pdf|access-date=2023-09-20|archive-date=2023-11-02|archive-url=https://web.archive.org/web/20231102041717/https://files.eric.ed.gov/fulltext/ED376173.pdf|url-status=live}}</ref>

[[Forensic engineering]] is an important technique of [[failure analysis]] that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

Reverse engineering attempts to discover the original problem-solving logic used in developing a product by disassembling the product and developing a plausible pathway to creating and assembling its parts.<ref>{{Cite web |url=https://litemind.com/problem-definition/|archive-url=https://web.archive.org/web/20170621145314/https://litemind.com/problem-definition/|archive-date=2017-06-21|title=Einstein's Secret to Amazing Problem Solving (and 10 Specific Ways You Can Use It)|website=Litemind|language=en-US|access-date=2017-06-11|date=2008-11-04 |last1=Passuello |first1=Luciano }}</ref>

=== Military science ===
In [[military Science|military science]], problem solving is linked to the concept of "end-states", the conditions or situations which are the aims of the strategy.<ref name="USJFCOM">{{cite web|date=27 October 2009|title=Commander's Handbook for Strategic Communication and Communication Strategy|url=http://www.au.af.mil/au/awc/awcgate/jfcom/cc_handbook_sc_27oct2009.pdf|archive-url=https://web.archive.org/web/20110429051434/http://www.au.af.mil/au/awc/awcgate/jfcom/cc_handbook_sc_27oct2009.pdf|archive-date=April 29, 2011|access-date=10 October 2016|publisher=[[United States Joint Forces Command]], Joint Warfighting Center, Suffolk, Va.}}</ref>{{rp|xiii, E-2}} Ability to solve problems is important at any [[military rank]], but is essential at the [[command and control]] level. It results from deep qualitative and quantitative understanding of possible scenarios. ''Effectiveness'' in this context is an evaluation of results: to what extent the end states were accomplished.<ref name="USJFCOM"/>{{rp|IV-24}} ''Planning'' is the process of determining how to effect those end states.<ref name="USJFCOM"/>{{rp|IV-1}}