From The Collaborative International Dictionary of English v.0.44 [gcide]:
Assertion \As*ser"tion\, noun [L. assertio, fr. asserere.]
1. The act of asserting, or that which is asserted; positive declaration or averment; affirmation; statement asserted; position advanced.
There is a difference between assertion and demonstration. --Macaulay.
2. Maintenance; vindication; as, the assertion of one's rights or prerogatives.
From WordNet (r) 2.0 [wn]:
noun
1: a declaration that is made emphatically (as if no supporting evidence were necessary) [syn: {averment}, {asseveration}]
2: the act of affirming or asserting or stating something [syn: {affirmation}, {statement}]
From Moby Thesaurus II by Grady Ward, 1.0 [moby-thes]:
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
From The Free On-line Dictionary of Computing (27 SEP 03) [foldoc]:
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)
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