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A polygon is a generalization of a 3-sided triangle, a 4-sided quadrilateral, and so on to n sides. A hypercube is a generalization of a 2-dimensional square, a 3-dimensional cube, and so on to n dimensions. A quadric, such as a hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to higher dimensions.
The full generalization rule allows for hypotheses to the left of the turnstile, but with restrictions.Assume is a set of formulas, a formula, and () has been derived. The generalization rule states that () can be derived if is not mentioned in and does not occur in .
Hasty generalization is the fallacy of examining just one or very few examples or studying a single case and generalizing that to be representative of the whole class of objects or phenomena. The opposite, slothful induction , is the fallacy of denying the logical conclusion of an inductive argument, dismissing an effect as "just a coincidence ...
Therefore, generalization is a valuable and integral part of learning and everyday life. Generalization is shown to have implications on the use of the spacing effect in educational settings. [13] In the past, it was thought that the information forgotten between periods of learning when implementing spaced presentation inhibited generalization ...
Olivier, Bousquet; Luxburg, Ulrike; Rätsch, Gunnar, eds. (2004). Advanced Lectures on Machine Learning.Lecture Notes in Computer Science. Vol. 3176. pp. 169–207.
Bird with earthworm: Shepard gives example of bird using "generalization," based on experience with one previous worm, to decide if another worm is edible. The universal law of generalization is a theory of cognition stating that the probability of a response to one stimulus being generalized to another is a function of the “distance ...
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In the first, most conceptual phase, McMaster and Shea show how generalization plays a central role in resolving the often conflicting goals of Cartographic design as a whole: functionality vs. aesthetics, information richness vs. clarity, and the desire to do more vs. the limitations of technology and medium. These conflicts can be reduced to ...