definition 1: therefore; for this reason; thus.
example: I don’t agree with the proposition, and hence I cannot vote for it.
definition 2: from this moment; from now.
example: Two years hence, the new building should be completed.
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Usage note: The word hence, in either of its meanings, tends to be used when speaking or writing in a formal style. In informal language, the two words “and hence” in the the first example would probably be replaced by “so”: I don’t agree with the proposition, so I can’t vote for it.