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Monotonicity of entailment is a property of many logical systems such that if a sentence follows deductively from a given set of sentences then it also follows deductively from any superset of those sentences.
A GQ is said to be non-monotone if it is neither monotone increasing nor monotone decreasing. An example of such a GQ is exactly three boys. Neither of the following sentences entails the other. Exactly three students ran. Exactly three students ran fast. The first sentence does not entail the second.
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ] [ 2 ] [ 3 ] This concept first arose in calculus , and was later generalized to the more abstract setting of order theory .
The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]
By the way, I'd say the first sentence in the Section "Monotonicity in calculus and analysis" is confusing. That is the definition of an increasing (or non-decreasing) function. A monotone function may be either increasing or decreasing (as defined in the next sentence). At least that is standard terminology in calculus textbooks.
The prosecutor argued in a monotone that she should be detained. But her defense attorney, an older man with glasses and a gray beard, responded that "she's not going to be a danger to anybody ...
A context that is neither downward nor upward entailing is non-monotone [citation needed], such as "exactly five." A downward-entailing operator reverses the relation of semantic strength among expressions. An expression like "run fast" is semantically stronger than the expression "run" since "John ran fast" entails "John ran," but not ...
If an agent has monotone preferences which means the marginal rate of substitution of the agent's indifference curve is positive. Given two products X and Y. If the agent is strictly preferred to X, it can get the equivalent statement that X is weakly preferred to Y and Y is not weakly preferred to X.