implication

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implication

Logic
a. the operator that forms a sentence from two given sentences and corresponds to the English if … then …
b. a sentence so formed. Usually written p→q or p⊃q, where p,q are the component sentences, it is true except when p (the antecedent) is true and q (the consequent) is false
c. the relation between such sentences

implication

[‚im·plə′kā·shən]
(mathematics)
The logical relation between two statements p and q, usually expressed as “if p then q.“
A logic operator having the characteristic that if p and q are statements, the implication of p and q is false if p is true and q is false, and is true otherwise. Also known as conditional implication; if-then operation; material implication.
References in periodicals archive ?
In [4], [5] and [8], the notions of prime filter, Boolean filter, implicative filters, normal filters, fantastic filters and positive implicative filters in BL-algebras were proposed, and the properties of the filters were investigated.
From the definition of implication filter and positive implicative filter, we can obtain the following corollary.
Outre l'observation participante a reference implicative dont les notes ont ete consignees, d'abord dans un carnet de terrain, puis transcrites et elaborees dans un journal de recherche, j'ai procede a quelques centaines d'entretiens informels au cours de plus de 60 jours de presence sur le terrain, de 1998 a 2001, ainsi qu'a des communications par telephone ou par Internet, a dix entrevues semi-dirigees, en equipe ou individuelles, avec six animatrices et deux animateurs des projets observes (lorsque cela etait possible, au moins deux entrevues avec les memes personnes) et une entrevue a la fin des projets avec dix-huit jeunes gens.
If an implicative complex of a metaphor is compelling enough (if the metaphor resonates in Black's term) the entailments (Lakoff & Johnson's term) of the secondary subject are ascribed to the primary subject in a more complete way.
Different types of complements to different types of implicative verbs will behave differently under negation:
For example, extremely brief tones, extremely dissonant tones, tones too distant in time from their implicative antecedents, or tones falling on an extremely weak part of the meter rarely create higher-level structures.
Do we need to examine the reverberation of war in order to make the soldier's experience meaningful, or is the examination of the soldier's role implicative enough?
Consider the causal statement A, written in implicative form (Suppes, 1958):
In this paper we define the notion of implicative filter.
He elides central events or leaves them offscreen, collapses fact and fiction, history and performance, moves between a multitude of characters without transitional devices, and fills his deep-focus, long-held compositions with so much quotidian detail that one's eye is left to roam a field of potential signifiers that may be mundane, even indifferent, but seem so implicative that they demand deciphering.
Other implicative points include discussions about the proletariat as a complement to the central regime of capital, where the existence of a center implies the existence of a periphery.
This implies, from the perspective of the first person imperfect verb form, that the presence of (3) in a dialect has little predictive or implicative value for what other features are found in it.