sequent

Definitions

  • WordNet 3.6
    • adj sequent following or accompanying as a consequence "an excessive growth of bureaucracy, with attendant problems","snags incidental to the changeover in management","attendant circumstances","the period of tension and consequent need for military preparedness","the ensuant response to his appeal","the resultant savings were considerable"
    • adj sequent in regular succession without gaps "serial concerts"
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Webster's Revised Unabridged Dictionary
    • Sequent A follower.
    • Sequent Following as an effect; consequent.
    • Sequent Following; succeeding; in continuance. "What to this was sequent Thou knowest already."
    • Sequent That which follows as a result; a sequence.
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Century Dictionary and Cyclopedia
    • sequent Continuing in the same course or order; following; succeeding.
    • sequent Following by natural or logical consequence.
    • n sequent A follower.
    • n sequent A sequence or sequel; that which follows as a result.
    • n sequent That which follows by an observed order of succession: used, in opposition to antecedent, where one wishes to avoid the implication of the relation of effect to cause that would be conveyed by the use of consequent.
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Chambers's Twentieth Century Dictionary
    • adjs Sequent following, succeeding
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Etymology

Webster's Revised Unabridged Dictionary
L. sequens, -entis, p. pr. of sequi, to follow. See Sue to follow
Chambers's Twentieth Century Dictionary
Fr.,—L. sequens, pr.p. of sequi, to follow.

Usage

In literature:

The situation had suddenly grown too confused for words, or even sequent thoughts.
"The Damnation of Theron Ware" by Harold Frederic
The kiss had bewildered her sequent sensations.
"Sandra Belloni, Complete" by George Meredith
She can beat me seven games out of twelve at chess; but the five I win sequently, for then I am awake.
"The Short Works of George Meredith" by George Meredith
Instead there should be twelve reports, so closely sequent as to sound as one string of explosion.
"Heart's Desire" by Emerson Hough
Cotyledones foliaceae, albae, amplae, curvat seminis sequentes: suturae placental, oppositae.
"Journals of Travels in Assam, Burma, Bhootan, Afghanistan and TheNeighbouring Countries" by William Griffith
A very similar kind of unification takes place between sequent images under the form of transformation.
"Illusions" by James Sully
Lower, come the opposing curves in the two boats, the whole forming one group of sequent lines up the whole side of the picture.
"The Harbours of England" by John Ruskin
Coronacio Henrici filii Regis Johannis apud Glouerniam qui Anno quarto sequente iterum coronatus est apud Westm'.
"A Chronicle of London from 1089 to 1483" by Anonymous
His voyage was the next Portuguese step sequent upon that of Bartholomew Dias.
"The Discovery of America Vol. 1 (of 2)" by John Fiske
They may be pursued much in the same way, or by alternations in which each prior study favors the sequent one.
"College Teaching" by Paul Klapper
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In poetry:

And, round the royal flag unfurled,
In sequent love and circling awe
The legions lead their living law,
And what was Chaos is a World:
"In War-Time: An Aspiration Of The Spirit" by Sydney Thompson Dobell
Yet, if the day should darken, or the storm
Beat on my brow, or shriek across the night,
And with God’s pregnant enmity inform
His sequent messengers of dark and light:
"Endeavour" by Robert Steel Byrnes
The sequent morn shall wake the sylvan quire;
The kid again shall wanton ere 'tis noon;
Nature will smile, will wear her best attire;
O let not gentle Delia smile so soon!
"Elegy XXV. To Delia, With Some Flowers" by William Shenstone

In science:

It remains to show that the sequent (θ ∧ θ[~z/~y] ⊢~x,~y ,~z ~y = ~z ) is provable in T.
Topological Galois Theory
This subtopos corresponds, by the duality theorem of , to a quotient T′ of T classified by the topos [A, Set], which can be characterized as the collection of all geometric sequents which hold in every model in A, that is, as T′ itself (as these models are jointly conservative for T′ by our hypothesis).
Topological Galois Theory
We shall establish the following fact, from which our thesis will follow at once: for any sequent σ := (φ ⊢~x ∨i∈I (∃ ~yi )θi ), σ holds in Mψ if and only if every arrow f : Mφ → Mψ in f.p.T-mod(Set) belongs to Sσ .
Topological Galois Theory
J -covering sieve on Mψ is maximal then any sequent σ which is provable in T′ is valid in Mψ ; indeed, if σ is provable in T′ then the cosieve Sσ is J -covering on Mφ and hence for any arrow f : Mφ → Mψ in f.p.T-mod(Set) the pullback cosieve f ∗(Sσ ) is J -covering on Mψ and hence maximal, i.e. f belongs to Sσ .
Topological Galois Theory
Each label names some sequent calculus rule, such as andl for ^-left.
Logic Programming, Functional Programming, and Inductive Definitions
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