SBVR — define 'is less than' on 'quantity'

Problem Description:

Clause 8.7 defines 'integer' as "a number with no fractional part". But the concept 'number' to which this definition appeals is not defined, and the entry does not cite a source for the definition. 'number' should be defined as well.

SBVR clause 8.7 defines the fact-type 'integer is-less-than integer'.
This is a narrow definition of the 'less-than' concept, which applies, with the same semantics, to 'numbers' and to arbitrary quantities. 'Quantity' is the general concept on which comparison for less and greater is defined for business purposes. It is the concept for which is-less-than should be defined in 8.7.

In Annex D, 'is less than' is used as a fact-type for prices and durations in several places, but it is never defined. This usage requires a wider definition of the is-less-than fact-type that is defined in 8.7, namely a definition on 'quantity'. D.2.3.3 defines 'duration' as "a quantity of time", but the term 'quantity' is not a vocabulary entry in either 8.7 or Annex D. And D.2.3.3 defines the fact-type 'duration is-at-most duration', but it has the same semantics as quantity is-less-than (or equal to) quantity. It is clear that this example is a model for the definition of "measurement" vocabularies, and 8.7 should provide the base term 'quantity' to support that.

• Proposed solution:

(1) define the term 'quantity' in SBVR, e.g.,
Definition: a determinate or estimated amount [of a thing]
Definition: the aspect in which a thing is measurable in terms of greater, less or equal
Source: MW
Note: The concept quantity can be elaborated into mathematical systems, such as integer and real numbers, and into systems of measures. This specification elaborates only the concepts for integer, because they are commonly used in structural rules (See x.x). For measurement systems and units of measure there are accepted vocabularies and perhaps standard ontologies, but the specification of such a vocabulary is beyond the scope of this specification.

(2) replace the the fact-type 'integer is-less-than integer' with the fact-type 'quantity is-less-than quantity'.

(3) add the concept 'number'
Definition: a [quantity] belonging to an abstract mathematical system and subject to laws of succession, addition and multiplication
Source: MW

(4) make integer a subtype of number, and number a subtype of quantity.

(5) correct the "term" style for 'number' in the definition of integer in 8.7, and for 'quantity' in the definition of duration in D.2.3.3.

(6) In D.2.3.3, add to the definition of duration is at most duration:
Synonymous form: duration is less than or equal to duration

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