sequent

1550s; borrowed from Middle French sequent, from Old French sequent, itself borrowed from Latin sequentem, present participle of sequī (“to follow”).[1]

• (UK) IPA^(key): /ˈsiːkwənt/

sequent (comparative more sequent, superlative most sequent)

1. (obsolete) That comes after in time or order; subsequent.
   • 1860, James Thomson (B.V.), Two Sonnets‎:

     Why are your songs all wild and bitter sad
     As funeral dirges with the orphans' cries?
     Each night since first the world was made hath had
     A sequent day to laugh it down the skies.

2. (now rare) That follows on as a result, conclusion etc.; consequent to, on, upon.
   • c. 1603–1604 (date written), William Shakespeare, “Measure for Measure”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC, [Act V, scene i]:

     But let my Triall, be mine owne Confession: / Immediate sentence then, and sequent death, / Is all the grace I beg.

   • 1897, Henry James, What Maisie Knew:

     Maisie found herself clutched to her mother's breast and passionately sobbed and shrieked over, made the subject of a demonstration evidently sequent to some sharp passage just enacted.

3. Recurring in succession or as a series; successive, consecutive.
   • c. 1603–1604 (date written), William Shakespeare, “The Tragedie of Othello, the Moore of Venice”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC, [Act I, scene ii]:

     The Gallies Haue sent a dozen sequent Messengers / This very night, at one anothers heeles: / And many of the Consuls, rais'd and met, / Are at the Dukes already.

• sequence

sequent (plural sequents)

1. Something that follows in a given sequence.
   • 1946, Bertrand Russell, History of Western Philosophy, I.30:

     The One is somewhat shadowy. It is sometimes called God, sometimes the Good; it transcends Being, which is the first sequent upon the One.

2. (logic) A disjunctive set of logical formulae which is partitioned into two subsets; the first subset, called the antecedent, consists of formulae which are valuated as false, and the second subset, called the succedent, consists of formulae which are valuated as true.[2] (The set is written without set brackets and the separation between the two subsets is denoted by a turnstile symbol, which may be read "give(s)".)

   A sequent ${\displaystyle a,b\vdash c,d}$ could be interpreted to correspond to an Existential Graph, whose expression in Existential Graph Interchange Format would be
   ~[(a) (b) ~[(c)] ~[(d)]], which in ordinary language could be expressed as "a and b give c or d".

3. (obsolete) A follower.
   • c. 1595–1596 (date written), William Shakespeare, “Loues Labour’s Lost”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, →OCLC, [Act IV, scene ii]:

     Sir Nathaniel, this Biron is one of the votaries with the king; and here he hath framed a letter to a sequent of the stranger queen's, which accidentally, or by the way of progression, hath miscarried.

4. (mathematics) A sequential calculus

• hypersequent
• sequent calculus

• “sequent”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• “sequent”, in The Century Dictionary […], New York, N.Y.: The Century Co., 1911, →OCLC.