Case analysis
Encyclopedia
Case analysis is one of the most general and applicable methods of analytical thinking, depending only on the division of a problem, decision or situation into a sufficient number of separate cases. Analysing each such case individually may be enough to resolve the initial question. The principle of case analysis is invoked in the celebrated remark of Sherlock Holmes
, to the effect that when one has eliminated the impossible, what remains must be true, however unlikely that seems.
: stringing together propositions with the logical connective
"or". Medical diagnosis
can indeed follow the Holmes pattern, with a patient's symptom possibly caused by a number of conditions: the patient suffers from A or B or ... or illness I; see differential diagnosis
. Deductive logic is applied to reducing the number of cases; see case-based reasoning
.
A canonical statement of case analysis in the sentential calculus is:
"If a statement P implies a statement Q, and a statement R also implies Q, and either P or R is true, then Q must be true."
and abuse of alcohol, with one factor not ruling out the other. This points up the distinction between exclusive or, and logical disjunction which is the default meaning of 'or' (in logic, mathematics and science) and which is non-exclusive. Case analysis of the non-overlapping kind is a special case, only.
That being said, in computer programming
, case analysis presents itself in a form best adapted to exclusive cases. In simple terms, the requirement is to have a list of actions, so that 'if X = 1 do P, if X = 2 do Q, if X = 3 do R' can be given as quite unambiguous instructions. The value of X here is computed according to what case one is in.
Two names for approaches that take complete case-by-case analysis as not meeting the needs of the topic under consideration are casuistry
, most often in ethics
, and the case study
method used in business schools.
Sherlock Holmes
Sherlock Holmes is a fictional detective created by Scottish author and physician Sir Arthur Conan Doyle. The fantastic London-based "consulting detective", Holmes is famous for his astute logical reasoning, his ability to take almost any disguise, and his use of forensic science skills to solve...
, to the effect that when one has eliminated the impossible, what remains must be true, however unlikely that seems.
Connections with logical principles
The logical roots of the Holmes remark speak to the principle of excluded middle. That indicates the importance to case analysis of logical disjunctionLogical disjunction
In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true. E.g. in this context, "A or B" is true if A is true, or if B is true, or if both A and B are...
: stringing together propositions with the logical connective
Logical connective
In logic, a logical connective is a symbol or word used to connect two or more sentences in a grammatically valid way, such that the compound sentence produced has a truth value dependent on the respective truth values of the original sentences.Each logical connective can be expressed as a...
"or". Medical diagnosis
Medical diagnosis
Medical diagnosis refers both to the process of attempting to determine or identify a possible disease or disorder , and to the opinion reached by this process...
can indeed follow the Holmes pattern, with a patient's symptom possibly caused by a number of conditions: the patient suffers from A or B or ... or illness I; see differential diagnosis
Differential diagnosis
A differential diagnosis is a systematic diagnostic method used to identify the presence of an entity where multiple alternatives are possible , and may also refer to any of the included candidate alternatives A differential diagnosis (sometimes abbreviated DDx, ddx, DD, D/Dx, or ΔΔ) is a...
. Deductive logic is applied to reducing the number of cases; see case-based reasoning
Case-based reasoning
Case-based reasoning , broadly construed, is the process of solving new problems based on the solutions of similar past problems. An auto mechanic who fixes an engine by recalling another car that exhibited similar symptoms is using case-based reasoning...
.
A canonical statement of case analysis in the sentential calculus is:
"If a statement P implies a statement Q, and a statement R also implies Q, and either P or R is true, then Q must be true."
Exhaustive analysis
The most important issue in this style of case analysis is that the cases should be collectively exhaustive: everything is covered. The condition that they should be exclusive, while convenient, is not to be assumed lightly; for example a patient's liver problem might be caused by hepatitisHepatitis
Hepatitis is a medical condition defined by the inflammation of the liver and characterized by the presence of inflammatory cells in the tissue of the organ. The name is from the Greek hepar , the root being hepat- , meaning liver, and suffix -itis, meaning "inflammation"...
and abuse of alcohol, with one factor not ruling out the other. This points up the distinction between exclusive or, and logical disjunction which is the default meaning of 'or' (in logic, mathematics and science) and which is non-exclusive. Case analysis of the non-overlapping kind is a special case, only.
That being said, in computer programming
Computer programming
Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...
, case analysis presents itself in a form best adapted to exclusive cases. In simple terms, the requirement is to have a list of actions, so that 'if X = 1 do P, if X = 2 do Q, if X = 3 do R' can be given as quite unambiguous instructions. The value of X here is computed according to what case one is in.
Other terminology
Case-by-case analysis is a more specific term for such a pinning-down of cases. It assumes a situation in which a thorough-going case analysis can be completed: all cases covered and resolved. This is not always realistic. Other forms of case analysis are best case analysis and worst case analysis, scenarios for the optimist and pessimist, respectively.Two names for approaches that take complete case-by-case analysis as not meeting the needs of the topic under consideration are casuistry
Casuistry
In applied ethics, casuistry is case-based reasoning. Casuistry is used in juridical and ethical discussions of law and ethics, and often is a critique of principle- or rule-based reasoning...
, most often in ethics
Ethics
Ethics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...
, and the case study
Case study
A case study is an intensive analysis of an individual unit stressing developmental factors in relation to context. The case study is common in social sciences and life sciences. Case studies may be descriptive or explanatory. The latter type is used to explore causation in order to find...
method used in business schools.
See also
- Mutually exclusiveMutually exclusiveIn layman's terms, two events are mutually exclusive if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both....
- Collectively exhaustiveCollectively exhaustiveIn probability theory, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the outcomes 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes.Another way...
- Pattern matchingPattern matchingIn computer science, pattern matching is the act of checking some sequence of tokens for the presence of the constituents of some pattern. In contrast to pattern recognition, the match usually has to be exact. The patterns generally have the form of either sequences or tree structures...
- Proof by exhaustionProof by exhaustionProof by exhaustion, also known as proof by cases, perfect induction, or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases and each case is checked to see if the proposition in question holds...