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Explanation-based learning ( EBL) is a form of machine learning that exploits a very strong, or even perfect, domain theory (i.e. a formal theory of an application domain akin to a domain model in ontology engineering, not to be confused with Scott's domain theory) in order to make generalizations or form concepts from training examples. [1]
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. This article is concerned with the inductive reasoning other than deductive reasoning (such as mathematical induction), where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the conclusion of ...
In algebra, generalizations of the derivative can be obtained by imposing the Leibniz rule of differentiation in an algebraic structure, such as a ring or a Lie algebra. Derivations. A derivation is a linear map on a ring or algebra which satisfies the Leibniz law (the product rule).
Operant conditioning. Operant conditioning, also called instrumental conditioning, is a learning process where voluntary behaviors are modified by association with the addition (or removal) of reward or aversive stimuli. The frequency or duration of the behavior may increase through reinforcement or decrease through punishment or extinction.
A scientific theory is an explanation of an aspect of the natural world and universe that can be (or a fortiori, that has been) repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, some theories are tested under controlled ...
The origins of class field theory lie in the quadratic reciprocity law proved by Gauss. The generalization took place as a long-term historical project, involving quadratic forms and their 'genus theory', work of Ernst Kummer and Leopold Kronecker/Kurt Hensel on ideals and completions, the theory of cyclotomic and Kummer extensions.
The fundamental theorem can be derived from Book VII, propositions 30, 31 and 32, and Book IX, proposition 14 of Euclid 's Elements . If two numbers by multiplying one another make some number, and any prime number measure the product, it will also measure one of the original numbers. — Euclid, Elements Book VII, Proposition 30.
Generalized conic. In mathematics, a generalized conic is a geometrical object defined by a property which is a generalization of some defining property of the classical conic. For example, in elementary geometry, an ellipse can be defined as the locus of a point which moves in a plane such that the sum of its distances from two fixed points ...