Changes between Initial Version and Version 1 of SigMmt/Templates/CardinalityAssignmentTemplates

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06/04/10 15:52:40 (11 years ago)
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  • SigMmt/Templates/CardinalityAssignmentTemplates

    v0 v1  
     1=== Base Templates !CardinalityEnd1Min, !CardinalityEnd1Max, !CardinalityEnd1MinMax, !CardinalityEnd2Min, !CardinalityEnd2Max, and !CardinalityEnd2MinMax === 
     2 
     3Are templates for expressing cardinality constraints on relations. 
     4[[br]] 
     5[[br]]!CardinalityEnd1MinMax(a, b) means that a is a relation and b and c are integers, and that 
     6[[br]]the first role of a has b as minimum, c as maximum cardinality. The other templates in this 
     7[[br]]group follow the same pattern. 
     8[[br]] 
     9[[br]]!CardinalityEnd1Min 
     10[[br]] 
     11[[br]]Roles: 
     12[[br]]1 hasRelationship !ClassOfRelationship 
     13[[br]]2 valMinimumCardinality INTEGER 
     14[[br]] 
     15[[br]]!CardinalityEnd1Max 
     16[[br]] 
     17[[br]]Roles: 
     18[[br]]1 hasRelationship !ClassOfRelationship 
     19[[br]]2 valMaximumCardinality INTEGER 
     20[[br]] 
     21[[br]]!CardinalityEnd1MinMax 
     22[[br]] 
     23[[br]]Roles: 
     24[[br]]1 hasRelationship !ClassOfRelationship 
     25[[br]]2 valMinimumCardinality INTEGER 
     26[[br]]3 valMaximumCardinality INTEGER 
     27[[br]] 
     28[[br]]!CardinalityEnd2Min 
     29[[br]] 
     30[[br]]Roles: 
     31[[br]]1 hasRelationship !ClassOfRelationship 
     32[[br]]2 valMinimumCardinality INTEGER 
     33[[br]] 
     34[[br]]!CardinalityEnd2Max 
     35[[br]] 
     36[[br]]Roles: 
     37[[br]]1 hasRelationship !ClassOfRelationship 
     38[[br]]2 valMaximumCardinality INTEGER 
     39[[br]] 
     40[[br]]!CardinalityEnd2MinMax 
     41[[br]] 
     42[[br]]Roles: 
     43[[br]]1 hasRelationship !ClassOfRelationship 
     44[[br]]2 valMinimumCardinality INTEGER 
     45[[br]]3 valMaximumCardinality INTEGER 
     46[[br]] 
     47[[br]]Axiom: 
     48[[br]] 
     49{{{ 
     50CardinalityEnd1Min(x1, x2) <-> 
     51ClassOfRelationship(x1) & 
     52INTEGER(x2) & 
     53exists u(CardinalityMin(u, x2) & hasEnd1Cardinality(x1, u)) . 
     54 
     55}}} 
     56[[br]]Axiom: 
     57[[br]] 
     58{{{ 
     59CardinalityEnd1Max(x1, x2) <-> 
     60ClassOfRelationship(x1) & 
     61INTEGER(x2) & 
     62exists u(CardinalityMax(u, x2) & hasEnd1Cardinality(x1, u)) . 
     63 
     64}}} 
     65[[br]]Axiom: 
     66[[br]] 
     67{{{ 
     68CardinalityEnd1MinMax(x1, x2, x3) <-> 
     69ClassOfRelationship(x1) & 
     70INTEGER(x2) & 
     71INTEGER(x3) & 
     72exists u(CardinalityMinMax(u, x2, x3) & 
     73hasEnd1Cardinality(x1, u)) . 
     74 
     75}}} 
     76[[br]]Axiom: 
     77[[br]] 
     78{{{ 
     79CardinalityEnd2Min(x1, x2) <-> 
     80ClassOfRelationship(x1) & 
     81INTEGER(x2) & 
     82exists u(CardinalityMin(u, x2)& 
     83hasEnd2Cardinality(x1, u)) . 
     84 
     85}}} 
     86[[br]]Axiom: 
     87[[br]] 
     88{{{ 
     89CardinalityEnd2Max(x1, x2) <-> 
     90ClassOfRelationship(x1) & 
     91INTEGER(x2) & 
     92exists u(CardinalityMax(u, x2)& 
     93hasEnd2Cardinality(x1, u)) . 
     94 
     95}}} 
     96[[br]]Axiom: 
     97[[br]] 
     98{{{ 
     99CardinalityEnd2MinMax(x1, x2, x3) <-> 
     100ClassOfRelationship(x1) & 
     101INTEGER(x2) & 
     102INTEGER(x3) & 
     103exists u(CardinalityMinMax(u, x2, x3)& 
     104hasEnd2Cardinality(x1, u)) . 
     105 
     106}}} 
     107[[br]]NOTE For unlimited minimum or maximum cardinalities, assign the values 0 and * cardinality, 
     108[[br]]respectively. See the definitions of templates !CardinalityMin, etc., above. 
     109[[br]] 
     110[[br]]NOTE What constitutes the first and second roles of a relation is stated in the table of prototemplates 
     111[[br]](D.1, page 103). 
     112[[br]] 
     113[[br]]NOTE Let R be a relation to which a cardinality n1 : m1 is assigned to the first role, and a cardinality 
     114[[br]]n2 : m2 to the second. This means that (1) each instance of the first role is R-related to at least 
     115[[br]]n2 and at most m2 distinct instances of the second role, and (2) each instance of the second role is 
     116[[br]]related to at least n1 and at most m1 distinct instances of the first role. 
     117[[br]] 
     118[[br]]EXAMPLE The statement !CardinalityEnd1MinMax(6 M8 bolt assembly, 6, 6) is suitable for expressing 
     119[[br]]an example of a constraint given in ISO 15926-2, clause 4.10.3, that “[t]he 
     120[[br]]class_of_relationship_with_signature ‘6 M8 bolt assembly’ has a cardinality such that each ‘6 of 
     121[[br]]M8 bolts’ is linked by exactly 6 relationships to different M8 bolts at all times”. The expansion of 
     122[[br]]this statement is shown in the following diagram. 
     123[[br]] 
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