Concepts inA note on a generalization of the Muddy Children puzzle
Generalization
A generalization of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic and human reasoning. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it is the essential basis of all valid deductive inferences. The process of verification is necessary to determine whether a generalization holds true for any given situation.
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Variety (universal algebra)
In mathematics, specifically universal algebra, a variety of algebras is the class of all algebraic structures of a given signature satisfying a given set of identities. Equivalently, a variety is a class of algebraic structures of the same signature which is closed under the taking of homomorphic images, subalgebras and (direct) products. In the context of category theory, a variety of algebras is usually called a finitary algebraic category.
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If and only if
¿ ¿ ¿ Logical symbolsrepresenting iff In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements. In that it is biconditional, the connective can be likened to the standard material conditional ("only if," equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other, i.e.
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Logic
Logic (from the Greek ¿¿¿¿¿¿ logik¿) is the philosophical study of valid reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, ontology, epistemology, and ethics.
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Child
Biologically, a child is generally a human between the stages of birth and puberty. Some vernacular definitions of a child include the fetus, as being an unborn child. The legal definition of "child" generally refers to a minor, otherwise known as a person younger than the age of majority.
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Solvable group
In mathematics, more specifically in the field of group theory, a solvable group (or soluble group) is a group that can be constructed from abelian groups using extensions. That is, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equation.
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Generalized quantifier
In linguistic semantics, a generalized quantifier is an expression that denotes a property of a property, also called a higher-order property. This is the standard semantics assigned to quantified noun phrases, also called determiner phrases, in short: DP. The DP every boy below says of a property X that the set of entities that are boys is a subset of the set of entities that have property X. So the following sentence says that the set of boys is a subset of the set of sleepers.
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Scientific modelling
Scientific modelling is the process of generating abstract, conceptual, graphical or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling. A scientific model can provide a way to read elements easily which have been broken down to a simpler form. Modelling is an essential and inseparable part of all scientific activity, and many scientific disciplines have their own ideas about specific types of modelling.
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