# SubQuantityOf¶

## Definition¶

«SubQuantityOf» is a parthood relation between two quantities, e.g.:

- alcohol is part of wine;
- plasma is part of blood;
- sugar is part of ice cream.

Quantities have not elements (or members). Since their members cannot be enumerated, they must be defined by a relation that unifies them into a connected whole (self-connectedness). Quantities are connected *topologically* (unlike e.g. collectives, which parts and members may not be placed together). *Topological connection* is characteristic for quantities and because of *topological connection,* sub-quantities cannot be shared among several super-quantities. For this reason, a subQuantityOf relation is always **non-sharable.** Since quantities do not have elements, they can be arbitrarily divided, like e.g. water. That´s why any quantity is defined to be *maximal portion* and can not be part of itself (water cannot be part of water). Since every part of a quantity is maximal (and self-connected), the SubQuantityOf parthood must have a **cardinality constraint of one and exactly one** in the sub-quantity side. E.g. since alcohol is a quantity (and, hence, maximal), there is exactly one quantity of alcohol which is part of a specific quantity of wine. Since quantity is *maximal,* it cannot have a quantity of the same kind as its part – i.e. the «SubQuantityOf» relation is **irreflexive**.

Nevertheless, a quantity can be part of another quantity (like glucose in wine) using the «SubQuantityOf» relation. The change of any of parts of the quantity changes the identity of the whole (i.e. quantities are *extensional* entities). That is why **the strong supplementation axiom** holds for the the «SubQuantityOf» relations (unlike «SubCollectionOf» relation, which on contrary holds only weaker axiom). For the same reason, all parts of a quantity are **essential** and «SubQuantityOf» relations are essential parthood relations. Further, since essential parthood relations are always transitive, «SubQuantityOf» is always **transitive**.

## Constraints¶

**C1:** The «SubQuantityOf» relation is always non-shareable.

**C2:** A sub-quantity is always an **essential part** of its super-quantity (marked with {essential} constraint).

**C3:** The cardinality in the part-end must be exactly one.

**C4:** The «SubQuantityOf» **quantities** at its both ends. Quantities are types as defined in the overview table above.

## Common questions¶

Ask us some question if something is not clear …

## Examples¶

**EX1:**

**EX2:**

**EX3:**

See also

- :ref:`part-whole
- «Containment»

**References:**

GUIZZARDI, Giancarlo. *Ontological Foundations for Structural Conceptual Models.* Enschede: CTIT, Telematica Instituut, 2005. GUIZZARDI, Giancarlo. *Introduction to Ontological Engineering.* [presentation] Prague: Prague University of Economics, 2011.