Relational System Shape

What it is

A RelationalSystemShape is a constraint specification that classifies entities in R by which predicates they carry and what those predicates must satisfy. It is what it means, in a RelationsSystem, for the object class to be closed under subobject formation — generative-closure condition 5.

A shape does not classify by declared type. It classifies by predicates: any entity that carries a given predicate is a target of that predicate’s shape, regardless of what else it is. What an entity IS is determined by which predicates it has, not by a category it declares membership in.

A shape is itself a RelationalEntity: it has id and description and is in R. The system can validate shapes using shapes. This is the self-referential closure condition 5 requires: the subobject classifier Ω is an object of R.

One shape per predicate

The constraint for predicate P lives in exactly one shape, targeting every entity that carries P. Multiple predicates on a single entity engage multiple shapes independently. An entity is never globally “valid” or “invalid” — it satisfies some shapes and not others, depending on which predicates it has. Validity is always relative to the shapes applicable at the current predicate set. A RelationalSystemShape CANNOT target entities by declared class membership. It CANNOT duplicate constraints already expressed by another shape — each shape is responsible for exactly one predicate. It CANNOT depend on predicates that are not themselves specced entities.

Open questions

• Whether shapes compose: if an entity carries both id and defines, is there a combined shape more than the sum of the two individual shapes? The current per-predicate model does not address composition.
• Whether the shape for a predicate should constrain the predicate value’s own required predicates (object constraints), or whether that is expressed by the value’s own shape.