The Collaborative International Dictionary of English v.0.48:

Abate \A*bate"\ ([.a]*b[=a]t"), v. t. [imp. & p. p. Abated, p.
   pr. & vb. n. Abating.] [OF. abatre to beat down, F.
   abattre, LL. abatere; ab or ad + batere, battere (popular
   form for L. batuere to beat). Cf. Bate, Batter.]
   1. To beat down; to overthrow. [Obs.]
      [1913 Webster]

            The King of Scots . . . sore abated the walls.
                                                  --Edw. Hall.
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   2. To bring down or reduce from a higher to a lower state,
      number, or degree; to lessen; to diminish; to contract; to
      moderate; to cut short; as, to abate a demand; to abate
      pride, zeal, hope.
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            His eye was not dim, nor his natural force abated.
                                                  --Deut. xxxiv.
                                                  7.
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   3. To deduct; to omit; as, to abate something from a price.
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            Nine thousand parishes, abating the odd hundreds.
                                                  --Fuller.
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   4. To blunt. [Obs.]
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            To abate the edge of envy.            --Bacon.
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   5. To reduce in estimation; to deprive. [Obs.]
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            She hath abated me of half my train.  --Shak.
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   6. (Law)
      (a) To bring entirely down or put an end to; to do away
          with; as, to abate a nuisance, to abate a writ.
      (b) (Eng. Law) To diminish; to reduce. Legacies are liable
          to be abated entirely or in proportion, upon a
          deficiency of assets.
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   To abate a tax, to remit it either wholly or in part.
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The Collaborative International Dictionary of English v.0.48:

Abate \A*bate"\ ([.a]*b[=a]t"), v. i. [See Abate, v. t.]
   1. To decrease, or become less in strength or violence; as,
      pain abates, a storm abates.
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            The fury of Glengarry . . . rapidly abated.
                                                  --Macaulay.
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   2. To be defeated, or come to naught; to fall through; to
      fail; as, a writ abates.
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   To abate into a freehold, To abate in lands (Law), to
      enter into a freehold after the death of the last
      possessor, and before the heir takes possession. See
      Abatement, 4.
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   Syn: To subside; decrease; intermit; decline; diminish;
        lessen.

   Usage: To Abate, Subside. These words, as here compared,
          imply a coming down from some previously raised or
          excited state. Abate expresses this in respect to
          degrees, and implies a diminution of force or of
          intensity; as, the storm abates, the cold abates, the
          force of the wind abates; or, the wind abates, a fever
          abates. Subside (to settle down) has reference to a
          previous state of agitation or commotion; as, the
          waves subside after a storm, the wind subsides into a
          calm. When the words are used figuratively, the same
          distinction should be observed. If we conceive of a
          thing as having different degrees of intensity or
          strength, the word to be used is abate. Thus we say, a
          man's anger abates, the ardor of one's love abates,
          "Winter's rage abates". But if the image be that of a
          sinking down into quiet from preceding excitement or
          commotion, the word to be used is subside; as, the
          tumult of the people subsides, the public mind
          subsided into a calm. The same is the case with those
          emotions which are tumultuous in their nature; as, his
          passion subsides, his joy quickly subsided, his grief
          subsided into a pleasing melancholy. Yet if, in such
          cases, we were thinking of the degree of violence of
          the emotion, we might use abate; as, his joy will
          abate in the progress of time; and so in other
          instances.
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The Collaborative International Dictionary of English v.0.48:

Abate \A*bate"\ ([.a]*b[=a]t"), n.
   Abatement. [Obs.] --Sir T. Browne.
   [1913 Webster]

WordNet (r) 3.0 (2006):

abate
    v 1: make less active or intense [syn: slake, abate,
         slack]
    2: become less in amount or intensity; "The storm abated"; "The
       rain let up after a few hours" [syn: abate, let up,
       slack off, slack, die away]

Moby Thesaurus II by Grady Ward, 1.0:

219 Moby Thesaurus words for "abate":
   ablate, abolish, abrade, abrogate, abstract, adjust to, allay,
   alleviate, allow, alter, anesthetize, annihilate, annul, appease,
   assuage, attemper, attenuate, bank the fire, bate, be eaten away,
   benumb, blot out, blunt, box in, charge off, chasten, circumscribe,
   close, condition, constrain, consume, consume away, control,
   corrode, cramp, cripple, crumble, curtail, cushion, cut, damp,
   dampen, de-emphasize, deaden, deaden the pain, debilitate, decline,
   decrease, deduct, deliquesce, depreciate, derogate, detract,
   devitalize, die away, die down, dilute, diminish, discount,
   disparage, dive, downplay, drain, drop, drop off, dull, dwindle,
   ease, ease matters, ease off, ease up, eat away, ebb, enervate,
   enfeeble, eradicate, erode, eviscerate, exhaust, extenuate,
   exterminate, extinguish, extirpate, extract, fall, fall away,
   fall off, file away, foment, give relief, gruel, hedge,
   hedge about, impair, invalidate, keep within bounds, kick back,
   languish, lay, lay low, leach, leaven, lenify, lessen, let down,
   let up, lighten, limit, loose, loosen, lull, make allowance,
   melt away, mitigate, moderate, modify, modulate, mollify, narrow,
   negate, nullify, numb, obtund, pad, palliate, play down, plummet,
   plunge, poultice, pour balm into, pour oil on, purify, qualify,
   quash, rattle, rebate, recede, reduce, reduce the temperature,
   refine, refund, regulate by, relax, relent, relieve, remit, remove,
   restrain, restrict, retrench, root out, rub away, run its course,
   run low, sag, salve, sap, season, set conditions, set limits,
   shake, shake up, shorten, shrink, sink, slack, slack off, slack up,
   slacken, slake, slow down, smother, sober, sober down, soften,
   soften up, soothe, stifle, stupe, subduct, subdue, subside,
   subtract, suppress, tail off, take a premium, take away, take from,
   take off, tame, taper, taper off, temper, thin, thin out,
   tone down, tune down, unbend, unbrace, undermine, underplay, undo,
   unman, unnerve, unstrain, unstrengthen, unstring, vitiate, wane,
   waste, waste away, water down, weaken, wear, wear away, weed,
   wipe out, withdraw, write off