The Collaborative International Dictionary of English v.0.48:

Implication \Im`pli*ca"tion\, n. [L. implicatio: cf. F.
   implication.]
   1. The act of implicating, or the state of being implicated.
      [1913 Webster]

            Three principal causes of firmness are. the
            grossness, the quiet contact, and the implication of
            component parts.                      --Boyle.
      [1913 Webster]

   2. An implying, or that which is implied, but not expressed;
      an inference, or something which may fairly be understood,
      though not expressed in words.
      [1913 Webster]

            Whatever things, therefore, it was asserted that the
            king might do, it was a necessary implication that
            there were other things which he could not do.
                                                  --Hallam.
      [1913 Webster]

WordNet (r) 3.0 (2006):

implication
    n 1: something that is inferred (deduced or entailed or
         implied); "his resignation had political implications"
         [syn: deduction, entailment, implication]
    2: a meaning that is not expressly stated but can be inferred;
       "the significance of his remark became clear only later";
       "the expectation was spread both by word and by implication"
       [syn: significance, import, implication]
    3: an accusation that brings into intimate and usually
       incriminating connection
    4: a logical relation between propositions p and q of the form
       `if p then q'; if p is true then q cannot be false [syn:
       implication, logical implication, conditional relation]
    5: a relation implicated by virtue of involvement or close
       connection (especially an incriminating involvement); "he was
       suspected of implication in several robberies"

The Free On-line Dictionary of Computing (19 January 2023):

implies
implication
imply

    (=> or a thin right arrow) A binary Boolean function
   and logical connective.  A => B is a true implication unless
   A is true and B is false.  The truth table is

    A B | A => B
    ----+-------
    F F |   T
    F T |   T
    T F |   F
    T T |   T

   It is surprising at first that A => B is always true if A is
   false, but if X => Y then we would expect that (X & Z) => Y
   for any Z.

   If A is actually an expression X & Y then the implication is
   called a syllogism.

   (2009-10-28)