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In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set; see the article Decidable language.
A decision problem whose input consists of strings or more complex values is formalized as the set of numbers that, via a specific Gödel numbering, correspond to inputs that satisfy the decision problem's criteria. A decision problem A is called decidable or effectively solvable if the formalized set of A is a recursive set.
An example of a decision problem is deciding with the help of an algorithm whether a given natural number is prime. Another example is the problem, "given two numbers x and y, does x evenly divide y?" A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.
A decision problem is a computational problem where the answer for every instance is either yes or no. An example of a decision problem is primality testing: "Given a positive integer n, determine if n is prime." A decision problem is typically represented as the set of all instances for which the answer is yes. For example, primality testing ...
With the establishment of modern decision theory in the 1950s, the model became a key ingredient in the formulation of non-probabilistic decision-making models in the face of severe uncertainty. [ 4 ] [ 5 ] It is widely used in diverse fields such as decision theory , control theory , economics , statistics , robust optimization , operations ...
Sample flowchart representing a decision process when confronted with a lamp that fails to light. In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the cognitive process resulting in the selection of a belief or a course of action among several possible alternative options.
Overconfidence effect, a tendency to have excessive confidence in one's own answers to questions. For example, for certain types of questions, answers that people rate as "99% certain" turn out to be wrong 40% of the time. [5] [44] [45] [46] Planning fallacy, the tendency for people to underestimate the time it will take them to complete a ...
Such examples are quite common and can include cases from everyday life, stories, or thought experiments, like Sartre's student or Sophie's Choice discussed in the section on examples. [10] The strength of arguments based on examples rests on the intuition that these cases actually are examples of genuine ethical dilemmas.