Application module: Set theory ISO/TS 10303-1210:2004(E)
© ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviations

4 Information requirements
   4.1 Required AM ARM
   4.2 ARM entity definitions
5 Module interpreted model
   5.1 Mapping specification
   5.2 MIM EXPRESS short listing

A MIM short names
B Information object registration
C ARM EXPRESS-G   EXPRESS-G
D MIM EXPRESS-G   EXPRESS-G
E Computer interpretable listings
Bibliography
Index

4 Information requirements

This clause specifies the information requirements for the Set theory application module. The information requirements are specified as the Application Reference Model (ARM) of this application module.

NOTE 1  A graphical representation of the information requirements is given in Annex C.

NOTE 2  The mapping specification is specified in 5.1. It shows how the information requirements are met by using common resources and constructs defined or imported in the MIM schema of this application module.

The following EXPRESS specification begins the Set_theory_arm schema and identifies the necessary external references.

EXPRESS specification:

*)
SCHEMA Set_theory_arm;
(*

4.1 Required AM ARM

The following EXPRESS interface statement specifies the elements imported from the ARM of another application module.

EXPRESS specification:

*)
USE FROM Class_arm;    --  ISO/TS 10303-1070
(*

NOTE 1   The schemas referenced above are specified in the following part of ISO 10303:

Class_arm ISO/TS 10303-1070

NOTE 2   See Annex C, Figures C.1and C.2 for a graphical representation of this schema.

4.2 ARM entity definitions

This subclause specifies the ARM entities for this module. Each ARM application entity is an atomic element that embodies a unique application concept and contains attributes specifying the data elements of the entity. The ARM entities and definitions are specified below.

4.2.1 Complement   EXPRESS-GMapping table

A Complement is a relationship that is between that indicates set S2 consists of all members of U that are not members of S1.

EXPRESS specification:

*)
ENTITY Complement;
  id : STRING;
  name : STRING;
  description : STRING;
  set_1 : Class;
  set_2 : Class;
  universe : Class;
END_ENTITY;
(*

Attribute definitions:

id: an identifier for the Complement relationship.

name: the word or sequence of words by which the Complement relationship is referenced.

description: the text that provides further information about the Complement relationship.

set_1: the Class that has set_2 as its complement within universe.

set_2: the Class that has set_1 as its complement within universe.

universe: the Class that is the union of set_1 and set_2.

4.2.2 Intersection   EXPRESS-GMapping table

An Intersection is a relationship that is between:

that indicates set R consists of each thing that is a member of each set within {Si}.

EXPRESS specification:

*)
ENTITY Intersection;
  id : STRING;
  name : STRING;
  description : OPTIONAL STRING;
  operand : SET[2:?] OF Class;
  resultant : Class;
END_ENTITY;
(*

Attribute definitions:

id: an identifier for the Intersection relationship.

name: the word or sequence of words by which the Intersection relationship is referenced.

description: the text that provides further information about the Intersection relationship. The value of the attribute need not be specified.

operand: the set of sets that have the resultant as their intersection.

resultant: the set that consists of each thing that is a member of each set within operand.

4.2.3 Power_set   EXPRESS-GMapping table

A Power_set is a relationship that is between: and that indicates S* is the set of all subsets of S.

EXPRESS specification:

*)
ENTITY Power_set;
  id : STRING;
  name : STRING;
  description : OPTIONAL STRING;
  base : Class;
  derived : Class;
END_ENTITY;
(*

Attribute definitions:

id: an identifier for the Power_set relationship.

name: the word or sequence of words by which the Power_set relationship is referenced.

description: the text that provides further information about the Power_set relationship. The value of the attribute need not be specified.

base: the set that is the union of the derived.

derived: the set of all subsets of the base.

4.2.4 Proper_subset   EXPRESS-GMapping table

A Proper_subset is a relationship that is between: that indicates:

EXPRESS specification:

*)
ENTITY Proper_subset;
  id : STRING;
  name : STRING;
  description : OPTIONAL STRING;
  subset : Class;
  superset : Class;
END_ENTITY;
(*

Attribute definitions:

id: an identifier for the Proper_subset relationship.

name: the word or sequence of words by which the Proper_subset relationship is referenced.

description: the text that provides further information about the Proper_subset relationship. The value of the attribute need not be specified.

subset: the Class that contains only members of superset.

superset: the Class that contains all members of subset.

4.2.5 Same_membership   EXPRESS-GMapping table

A Same_membership is a relationship that is between

that indicates the sets have the same members, that is they are equal.

EXPRESS specification:

*)
ENTITY Same_membership;
  id : STRING;
  name : STRING;
  description : OPTIONAL STRING;
  set_1 : Class;
  set_2 : Class;
END_ENTITY;
(*

Attribute definitions:

id: an identifier for the Same_membership relationship.

name: the word or sequence of words by which the Same_membership relationship is referenced.

description: the text that provides further information about the Same_membership relationship. The value of the attribute need not be specified.

set_1: the class that contains the same members as set_2.

set_2: the class that contains the same members as set_1.

4.2.6 Subset   EXPRESS-GMapping table

A Subset is a relationship that is between: that indicates:

EXPRESS specification:

*)
ENTITY Subset;
  id : STRING;
  name : STRING;
  description : OPTIONAL STRING;
  subset : Class;
  superset : Class;
END_ENTITY;
(*

Attribute definitions:

id: an identifier for the Subset relationship.

name: the word or sequence of words by which the Subset relationship is referenced.

description: the text that provides further information about the Subset relationship. The value of the attribute need not be specified.

subset: the class that contains only members of superset.

superset: the class that contains all members of subset.

4.2.7 Union   EXPRESS-GMapping table

A Union is a relationship that is between: that indicates set R consists of each thing that is a member of any set within {Si}.

EXPRESS specification:

*)
ENTITY Union;
  id : STRING;
  name : STRING;
  description : OPTIONAL STRING;
  operand : SET[2:?] OF Class;
  resultant : Class;
END_ENTITY;
(*

Attribute definitions:

id: an identifier for the Union relationship.

name: the word or sequence of words by which the Union relationship is referenced.

description: the text that provides further information about the Union relationship. The value of the attribute need not be specified.

operand: the set of sets that have the resultant as their union.

resultant: the set that consists of each thing that is a member of any set within operand.



*)
END_SCHEMA;  -- Set_theory_arm
(*

© ISO 2004 — All rights reserved