Not sure what the formal name for this is, @dosumis calls this axiom relaxation

Motivation

It is frequently convenient to view an ontology without equivalence axioms. This is often for structural reasons. Certain editions of ontologies may come with a guarantee that the existential graph formed by all SubClassOf axioms (between named classes and existential axioms) is both complete (w.r.t graph operations) and non-redundant. Including EquivalentClasses axioms can introduce redundancy at the graph view level. For example, the genus is frequently more general than the inferred superclasses.

To ensure that the existential graph is graph-complete it's necessary to write new SubClassOf axioms that are entailed by (but weaker than) Equivalence axioms

Basic Operation

For any equivalence axiom between a name class C and either a single existential X_1 or the class expression IntersectionOf(X_1 ... X_n), generate axioms

• C SubClassOf X_1
• ...
• C SubClassOf X_n

This could possibly be conceived of as the chaining of two operations: (1) weakening of an equivalence to a SubClassOf (2) rewriting a C SubClassOf IntersectionOf(...) axiom to multiple subclass axioms. However, there should be a way to present this to the user as a single operation.

Extensions

The basic operation could be extended to axioms involving arbitrary numbers of named classes and at least one existential. It would also be valid to rewrite equivalents between two named classes as reciprocal subClassOf axioms, but there is no requirement to do so at present so I recommend sticking with the basic.