# Changes between Initial Version and Version 1 of SigMmt/Templates/CardinalityTemplates

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06/05/10 16:06:22 (10 years ago)
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• ## SigMmt/Templates/CardinalityTemplates

v0 v1
1=== Base Templates !CardinalityMin, !CardinalityMax, !CardinalityMinMax ===
2
3[[br]]!CardinalityMin, !CardinalityMax, and !CardinalityMinMax are templates for expressing the
4[[br]]values of cardinalities.
5[[br]]
6[[br]]!CardinalityMinMax(a, b, c) means that a is a cardinality and b and c are integers, and that
7[[br]]b is the minimal, c the maximal, constraint of a. !CardinalityMin and !CardinalityMax are
8[[br]]similar, and apply to just the minimal, resp. the maximal constraint.
9[[br]]!CardinalityMin
10[[br]]
11[[br]]Roles:
12[[br]]1 hasCardinality Cardinality
13[[br]]2 valMinimumCardinality INTEGER
14[[br]]
15[[br]]!CardinalityMax
16[[br]]
17[[br]]Roles:
18[[br]]1 hasCardinality Cardinality
19[[br]]2 valMaximumCardinality INTEGER
20[[br]]
21[[br]]!CardinalityMinMax
22[[br]]
23[[br]]Roles:
24[[br]]1 hasCardinality Cardinality
25[[br]]2 valMinimumCardinality INTEGER
26[[br]]3 valMaximumCardinality INTEGER
27
28Axiom:
29{{{
30CardinalityMin(x1, x2) <->
31Cardinality(x1) &
32INTEGER(x2) &
33hasMinimumCardinality(x1, x2) .
34}}}
35
36Axiom:
37{{{
38CardinalityMax(x1, x2) <->
39Cardinality(x1) &
40INTEGER(x2) &
41hasMaximumCardinality(x1, x2) .
42}}}
43
44Axiom:
45{{{
46CardinalityMinMax(x1, x2, x3) <->
47Cardinality(x1) &
48INTEGER(x2) &
49INTEGER(x3) &
50CardinalityMin(x1, x2) &
51CardinalityMax(x1, x3) .
52}}}
53
54NOTE In ISO 15926, cardinalities are first-class objects. In ISO 15926-2, it is stated that an absence
55of specified minimum or maximum values for a cardinality should be interpreted as a absence
56of constraints (clause 5.2.13.1). The nature of the representation of ISO 15926-2 in first-order logic, with an open world assumption, mandates that both lower and upper bounds be given explicitly.
57Where no minimal constraint applies, the value 0 should be assigned. Where no maximum constraint applies, the reference item * Cardinality should be assigned (see 8.2.1).