The Collaborative International Dictionary of English v.0.48:

Presume \Pre*sume"\, v. i.
   1. To suppose or assume something to be, or to be true, on
      grounds deemed valid, though not amounting to proof; to
      believe by anticipation; to infer; as, we may presume too
      far.
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   2. To venture, go, or act, by an assumption of leave or
      authority not granted; to go beyond what is warranted by
      the circumstances of the case; to venture beyond license;
      to take liberties; -- often with on or upon before the
      ground of confidence.
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            Do not presume too much upon my love. --Shak.
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            This man presumes upon his parts.     --Locke.
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The Collaborative International Dictionary of English v.0.48:

Presume \Pre*sume"\, v. t. [imp. & p. p. Presumed; p. pr. &
   vb. n. Presuming.] [F. pr['e]sumer, L. praesumere,
   praesumptum; prae before + sumere to take. See Assume,
   Redeem.]
   1. To assume or take beforehand; esp., to do or undertake
      without leave or authority previously obtained.
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            Dare he presume to scorn us in this manner? --Shak.
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            Bold deed thou hast presumed, adventurous Eve.
                                                  --Milton.
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   2. To take or suppose to be true, or entitled to belief,
      without examination or proof, or on the strength of
      probability; to take for granted; to infer; to suppose.
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            Every man is to be presumed innocent till he is
            proved to be guilty.                  --Blackstone.
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            What rests but that the mortal sentence pass, . . .
            Which he presumes already vain and void,
            Because not yet inflicted?            --Milton.
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WordNet (r) 3.0 (2006):

presume
    v 1: take to be the case or to be true; accept without
         verification or proof; "I assume his train was late" [syn:
         assume, presume, take for granted]
    2: take upon oneself; act presumptuously, without permission;
       "How dare you call my lawyer?" [syn: make bold, dare,
       presume]
    3: constitute reasonable evidence for; "A restaurant bill
       presumes the consumption of food"
    4: take liberties or act with too much confidence