Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 v. To establish a set of axioms that describe or govern certain phenomena
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

It is impossible to axiomatize what "natural" means in any consistent way.
An Argument from Realism Against Naturalism about Human Beings

For our current purposes, it is convenient to axiomatize this logic as a natural deduction system, taking all tautologies as axioms and the familiar natural deduction rules governing the singular quantifiers and the identity sign as rules of inference.

If I would axiomatize science I would try to establish the process and its objects.
More incredible chutzpah from John Mark Reynolds  The Panda's Thumb

These five rules therefore completely axiomatize equational logic in the sense that every consequence of a set A of equations can be produced from A via finitely many applications of these five rules.

Actually one is able to axiomatize tnorm based systems for some particular classes of tnorms.

In the early 1900s it became clear that one has to state precisely what basic assumptions are made in Set Theory; in other words, the need has arisen to axiomatize Set Theory.

Lisp wasn't designed to fix the mistakes in Fortran; it came about more as the byproduct of an attempt to axiomatize computation.

The deeper point here is that today we seek to axiomatize all our assumptions, and accept nothing as truth merely on the basis of “reality” or “common sense.”

Bertrand Russell had already published, in Principia Mathematica (191013), a massive attempt to axiomatize mathematics in a consistent way.

(iii) It could help us decide whether some list of equational laws intended to axiomatize the integers is complete in the sense that any equation holding of the integers follows from the laws in that list.
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