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

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

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 (19 January 2023):

axiom

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

   Compare: lemma.

   (1995-03-31)