Axiomatic replacement
Definition
Axiomatic replacement changes or explicitly restates the premises and rules a solution is allowed to use.
Explanation
A familiar proof can become a different task when the problem specifies an unfamiliar formal system or requires properties to be derived from stated axioms. A solution must then justify its steps from that system rather than import an unstated textbook result.
For the instructor, the rubric matters as much as the wording. If students are asked to work from specified axioms, the grading should check that they do so. Renaming a system alone does not establish that its mathematics has changed or that a model has never encountered it.
When reviewing a response, compare the assumptions it uses with the assumptions the question permits. That check can identify a reversion to a familiar result.
Scope and evidence
The AIED work uses this term for an assignment perturbation strategy. A plausible explanation involving familiar patterns should not be stated as verified memorization or knowledge of a proprietary training corpus.
Related concepts
Axiom reversion · Iterative perturbation process · One-Shot GenAI Resistance