SYSML14 — SysML: Unts and QualityKind

Currently, QuanttiyKind can only be part of 1 SystemOfQuantities.

This seems wrong. For example, wouldn’t the amp and abamp, one is the SI unit and other being the emu-cgs unit of current, have the same quantity kind, current, but they might be in different SystemofQuantities.

This exclusive association would prevent reusing existing definitions of Units & QuantityKinds for custom systems.

This issue involves three problems related to reuse:
1) Currently, multiplicities between Unit (resp. QuantityKind) and SystemOfUnits
(resp. SystemOfQuantities) prevent reusing the same definitions of Units and
Quantities across multiple systems of these.
2) Defining units and quantity kinds as specializations of others is an important
reuse use case.
3) Defining units for quantities of dimension one due to such quantities
representing a number of entities or a ratio of two quantities of the same kind.
In both cases, Per ISO 80000-1 and VIM, the coherent derived unit for such
quantities is the number one. This raises the question whether there is a unit
“one” or not.
(1) Enabling reuse:
The resolution of issue 18681 in ballot 5 showed an updated Figure D.8 where the
association-owned end multiplicities made it clear that, as of SysML 1.3, a Unit and a
QuantityKind can be associated to at most one SystemOfUnits and
SystemOfQuantities respectively even though these associations are non-composite.
In practice, the 0-1 multiplicity on these associations precludes reusing existing
model library definitions of Units and QuantityKinds such as ‘metre’ and ‘length’ from
SysML’s ISO 80000-1 model library. There are three forms of reuse:
a) reusing the same definition in different systems b) defining a system to include all the definitions from another system
c) defining a system to reuse selected definitions from another system
For the first form of reuse, the 0-1 association-owned end multiplicities need to be
relaxed to 0..*. For the second and third form of reuse, it is necessary to introduce
new associations for a system of units or quantities to include or reuse zero or more
other system of units or quantities.
(2) Reuse and specialization for general quantities and units
Currently, QUDV provides limited support for defining a quantity kind as a
specialization of another (see ISO 80000-1, 3.1 and 3.2 Notes for examples).
Unfortunately, this capability is only available for a SpecializedQuantityKind. This
means that, for example, it is not possible to define a DerivedQuantityKind as a
specialization of another QuantityKind. A similar capability is needed for Units: for
two quantity kinds QK1 and QK2, if QK1 is a specific quantity kind for the generic
quantity kind QK2, then the unit U1 corresponding to QK1 ought to be a specific unit
for the generic unit U2 corresponding to QK2.
(3) Reuse and specialization related to quantities of dimension one
This involves two cases:
a) Derived quantities of dimension one
Derived quantities that are intrinsically defined as indexes, levels, numbers or
ratios all have dimension one (see ISO 80000-1, 3.8 and Annexes A3, A4).
Specializing quantities of dimension one motivates adding a capability for
specializing the corresponding units. For example, ISO 80000-1 3.8 and 3.9
mention radian as an example of a derived unit for a quantity of dimension 1
(i.e., plane angle whose dimension is length/length). However, it is also
possible to define a SystemOfUnits/ Quantities in which radian is defined as a
base unit for plane angle, a base quantity. In such a system, there is no
UnitFactor nor any QuantityKindFactor available to determine that plane angle
is a quantity with dimension one unless it is explicitly asserted.
b) Quantities representing a number of entities
Quantities that intrinsically represent a number of entities have dimension one;
however such quantities carry more information than just a number per ISO
80000-1, 3.8 Note 4. Accounting for this information requires adding a
capability for designating a particular Unit as the unitary value for quantity
representing a number of entities.
This resolution addresses all 3 aspects of reuse described above by refactoring
QUDV to:

• enable defining a Unit or QuantityKind as a specialization of possibly multiple
  Units or QuantityKinds respectively, designate a Unit as representing a unit count of entities,
• designate a QuantityKind as representing a number of entities,
• designate a QuantityKind as representing a quantity of dimension one.
  This refactoring helps avoid defining a unit “one” explicitly as the unit for all quantities
  of dimension one. Doing so would have resulted in a widely reused unit “one” that
  would carry no useful information (ISO 80000-1, 3.8 Note 2). Instead, the explicit
  “quantity of dimension one” designation capability puts the emphasis on defining a
  meaningful unit for such a quantity.
  See the resolution to issue 18724 which addresses the potential problems involved in
  reusing systems of units and quantity kinds as well as the need for refactoring the
  modeling of Unit::primaryQuantityKind. For changes pertaining to
  Unit::primaryQuantityKind, see the resolution to issue 18724