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

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Timestamp:
06/05/10 16:06:22 (10 years ago)
Author:
onnopaap (IP: 84.104.92.156)
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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).  
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