The Collaborative International Dictionary of English v.0.48:

Assertion \As*ser"tion\, n. [L. assertio, fr. asserere.]
   1. The act of asserting, or that which is asserted; positive
      declaration or averment; affirmation; statement asserted;
      position advanced.
      [1913 Webster]

            There is a difference between assertion and
            demonstration.                        --Macaulay.
      [1913 Webster]

   2. Maintenance; vindication; as, the assertion of one's
      rights or prerogatives.
      [1913 Webster]

WordNet (r) 3.0 (2006):

assertion
    n 1: a declaration that is made emphatically (as if no
         supporting evidence were necessary) [syn: assertion,
         averment, asseveration]
    2: the act of affirming or asserting or stating something [syn:
       affirmation, assertion, statement]

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

assertion

    1. An expression which, if false, indicates an
   error.  Assertions are used for debugging by catching
   can't happen errors.

   2. In logic programming, a new fact or rule added to the
   database by the program at run time.  This is an
   extralogical or impure feature of logic programming
   languages.

   (1997-06-30)