déquivalence

Déquivalence is a term that appears in some scholarly contexts as a counterpart or companion concept to equivalence, but it is not widely standardized across disciplines. The word is formed from dé- and équivalence, suggesting notions of negation, reversal, refinement, or reassessment of an established equivalence relation. Because its meaning is not fixed, its precise interpretation varies by field and author.

In mathematics, déquivalence is sometimes used informally to describe actions that modify an existing equivalence relation. Common themes include moving from a coarse partition to a finer one by introducing a stronger relation that distinguishes elements previously identified as equivalent. In this sense, déquivalence can be viewed as a process of refinement — breaking identifications to obtain more granular classes. Some discussions may also treat déquivalence as the opposite of quotienting, i.e., seeking data or structure that has been collapsed by an equivalence relation, though this usage is not standard.

In other disciplines such as computer science, logic, or data analysis, the term may appear in a looser sense to denote rechecking or challenging assumed equivalences between objects, representations, or models. Here, déquivalence emphasizes critical examination of when two items should be regarded as equivalent, and may lead to a redefinition of criteria for equivalence or to the recovery of distinguishing information that was previously collapsed.

Overall, déquivalence is a flexible, field-dependent notion that generally concerns altering or reevaluating established equivalence relations rather than establishing a universally accepted formal concept.

See also: equivalence relation, partition, refinement, quotient set, model comparison.