The Collaborative International Dictionary of English v.0.48:

Axiom \Ax"i*om\, n. [L. axioma, Gr. ? that which is thought
   worthy, that which is assumed, a basis of demonstration, a
   principle, fr. ? to think worthy, fr. ? worthy, weighing as
   much as; cf. ? to lead, drive, also to weigh so much: cf F.
   axiome. See Agent, a.]
   1. (Logic & Math.) A self-evident and necessary truth, or a
      proposition whose truth is so evident as first sight that
      no reasoning or demonstration can make it plainer; a
      proposition which it is necessary to take for granted; as,
      "The whole is greater than a part;" "A thing can not, at
      the same time, be and not be."
      [1913 Webster]

   2. An established principle in some art or science, which,
      though not a necessary truth, is universally received; as,
      the axioms of political economy.
      [1913 Webster]

   Syn: Axiom, Maxim, Aphorism, Adage.

   Usage: An axiom is a self-evident truth which is taken for
          granted as the basis of reasoning. A maxim is a
          guiding principle sanctioned by experience, and
          relating especially to the practical concerns of life.
          An aphorism is a short sentence pithily expressing
          some valuable and general truth or sentiment. An adage
          is a saying of long-established authority and of
          universal application.
          [1913 Webster] Axiomatic

WordNet (r) 3.0 (2006):

axiom
    n 1: a saying that is widely accepted on its own merits [syn:
         maxim, axiom]
    2: (logic) a proposition that is not susceptible of proof or
       disproof; its truth is assumed to be self-evident

Moby Thesaurus II by Grady Ward, 1.0:

173 Moby Thesaurus words for "axiom":
   a belief, a priori principle, a priori truth, absolute fact,
   accepted fact, actual fact, adage, admitted fact, affirmation, ana,
   analects, aphorism, apothegm, apriorism, article of faith,
   assertion, assumed position, assumption, bald fact, bare fact,
   basis, brocard, brutal fact, byword, canon, catchword,
   categorical proposition, center, circumstance, cold fact,
   collected sayings, conceded fact, conjecture, core, current saying,
   data, datum, demonstrable fact, dictate, dictum, distich, doctrine,
   dogma, elixir, empirical fact, epigram, essence, essential,
   established fact, expression, fact, fact of experience,
   first principles, flower, focus, formula, foundation, fundamental,
   gist, given fact, gnome, golden rule, golden saying, gravamen,
   ground, guesswork, hard fact, heart, hypostasis, hypothesis,
   hypothesis ad hoc, indisputable fact, inescapable fact, inference,
   inner essence, kernel, law, lemma, major premise, marrow,
   matter of fact, maxim, meat, minor premise, moral, mot, motto,
   naked fact, not guesswork, not opinion, nub, nucleus,
   nuts and bolts, oracle, philosopheme, philosophical proposition,
   phrase, pith, pithy saying, plain, position, positive fact,
   postulate, postulation, postulatum, precept, premise, prescript,
   presumption, presupposal, presupposition, principium, principle,
   proposition, propositional function, provable fact, proverb,
   proverbial saying, proverbs, quid, quiddity, quintessence, rule,
   salient fact, sap, saw, saying, self-evident fact,
   self-evident truth, sentence, sententious expression,
   set of postulates, settled principle, significant fact,
   simple fact, sloka, sober fact, soul, spirit, statement,
   stock saying, stubborn fact, stuff, substance, sumption, supposal,
   supposing, supposition, surmise, sutra, teaching, tenet, text,
   the case, the nitty-gritty, theorem, thesis, truism, truth,
   truth table, truth-function, truth-value, undeniable fact,
   universal truth, verse, well-known fact, wisdom, wisdom literature,
   wise saying, witticism, word, words of wisdom,
   working hypothesis



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

AXIOM

    A commercially available subset of the
   Scratchpad, symbolic mathematics system from IBM.

   ["Axiom - The Scientific Computing System", R. Jenks et al,
   Springer 1992].

   [Relationship with AXIOM*?]

   (1995-02-21)


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

axiom

    A well-formed formula which is taken to be true
   without proof in the construction of a theory.

   Compare: lemma.

   (1995-03-31)