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In mathematical logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them. [1] Formulas from a formal theory are "realized" by objects, known as "realizers", in a way that knowledge of the realizer gives knowledge about the truth of the formula.
In probability and statistics, a realization, observation, or observed value, of a random variable is the value that is actually observed (what actually happened). The random variable itself is the process dictating how the observation comes about.
Zermelo's axioms incorporated the principle of limitation of size to avoid Russell's paradox. In 1910, the first volume of Principia Mathematica by Russell and Alfred North Whitehead was published. This seminal work developed the theory of functions and cardinality in a completely formal framework of type theory , which Russell and Whitehead ...
Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates.Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, then the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances ...
In a large class of singularly perturbed problems, the domain may be divided into two or more subdomains. In one of these, often the largest, the solution is accurately approximated by an asymptotic series [2] found by treating the problem as a regular perturbation (i.e. by setting a relatively small parameter to zero).
Markov's principle (also known as the Leningrad principle [1]), named after Andrey Markov Jr, is a conditional existence statement for which there are many equivalent formulations, as discussed below. The principle is logically valid classically, but not in intuitionistic constructive mathematics. However, many particular instances of it are ...
In accounting, the revenue recognition principle states that revenues are earned and recognized when they are realized or realizable, no matter when cash is received. It is a cornerstone of accrual accounting together with the matching principle. Together, they determine the accounting period in which revenues and expenses are recognized. [1]
The resolution rule in propositional logic is a single valid inference rule that produces a new clause implied by two clauses containing complementary literals. A literal is a propositional variable or the negation of a propositional variable.