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]

Moby Thesaurus II by Grady Ward, 1.0:

107 Moby Thesaurus words for "assertion":
   Parthian shot, a priori principle, address, admission, affidavit,
   affirmance, affirmation, allegation, announcement, annunciation,
   answer, apostrophe, apriorism, asseveration, assumed position,
   assumption, attest, attestation, averment, avouchment, avowal,
   axiom, basis, categorical proposition, comment, compurgation,
   conclusion, confirmation, contention, crack, creed, data,
   declaration, deposition, dictum, disclosure, enunciation,
   exclamation, expression, first principles, foundation, greeting,
   ground, hypothesis, hypothesis ad hoc, insistence,
   instrument in proof, interjection, ipse dixit, legal evidence,
   lemma, major premise, manifesto, mention, minor premise, note,
   observation, philosopheme, philosophical proposition, phrase,
   position, position paper, positive declaration, postulate,
   postulation, postulatum, predicate, predication, premise,
   presupposition, proclamation, profession, pronouncement,
   proposition, propositional function, protest, protestation,
   question, reflection, remark, representation, say, say-so, saying,
   sentence, stance, stand, statement, subjoinder, sumption, supposal,
   sworn evidence, sworn statement, sworn testimony, testimonial,
   testimonium, testimony, theorem, thesis, thought, truth table,
   truth-function, truth-value, utterance, vouch, witness, word



The Free On-line Dictionary of Computing (30 December 2018):

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)