• a possible_individual_during_period, which is a iso15926-2:possible_individual that lasts for a period of time;
• a possible_individual_at_instant, which is a iso15926-2:possible_individual that exists at an instant.

[iso15926-2:temporal_part_of :MyLine ;
 iso15926-x:during
       [ topology:end_1_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T10:00" ] ;
         topology:end_2_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T11:00" ] ] ]
  myOnt:transmitted_energy  [ a            iso31:energy ;
                              scale:kWh    [ basics:decimal  "12300" ] ] .

[iso15926-2:temporal_part_of :MyLine ;
 iso15926-x:at_instant
       [ iso15926-x:utc_iso8601 "2007-03-14T10:30"  ] ]
  myOnt:active_power  [ a            iso31:power ;
                        scale:kW     [ basics:decimal  "14500" ] ] .

A physical property that is valid for an instant can be associated with a possible_individual_during_period indirectly in the following ways:

• as a derived property such as the mean, maximum or minimum over the period;
• as a function over a 1D manifold of instances of possible_individual_at_instant within the possible_individual_during_period.

These two approaches are related, because mean, maximum and minimum are properties of the function.

A possible_individual_during_period can have the same physical property at each instant. This does not mean that the possible_individual_during_period has the property, but instead that the function over the 1D manifold of instances of possible_individual_at_instant is a basics:constant_function.

EXAMPLE 3 Consider the transmitted power function over time for "MyLine", that is shown in Figure 4.

Figure 4: Transmitted power function over time

The following statements can be made:

• the function from 10:00 to 11:00 is constant with value 10000 kW;
• the function from 11:00 to 12:00 is constant with value 15000 kW;
• the function from 10:00 to 12:00 has the mean value 12500 kW.

These statements can be recorded as follows:

:MyLine_from_2007-03-14T10:00_to_11:00
  iso15926-2:temporal_part_of :MyLine ;
  iso15926-x:during
       [ topology:end_1_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T10:00" ] ;
         topology:end_2_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T11:00" ] ]
  a                           topology:directed_manifold_edge .

:MyLine_from_2007-03-14T11:00_to_12:00
  iso15926-2:temporal_part_of :MyLine ;
  iso15926-x:during
       [ topology:end_1_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T11:00" ] ;
         topology:end_2_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T12:00" ] ]
  a                           topology:directed_manifold_edge .

:MyLine_from_2007-03-14T10:00_to_12:00
  iso15926-2:temporal_part_of :MyLine ;
  iso15926-x:during
       [ topology:end_1_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T10:00" ] ;
         topology:end_2_of_edge  [ iso15926-x:utc_iso8601 "2007-03-14T12:00" ] ]
  a                           topology:directed_manifold_edge .

[ a                  basics:constant_function ;
  rdfs:domain        :MyLine_from_2007-03-14T10:00_to_11:00 ;
  rdfs:range         iso31:power ;
  rdfs:subPropertyOf myOnt:active_power ;
  basics:value_of_constant_function
                     [ a           iso31:power ;
                       scale:kW  [ basics:decimal  "10000" ] ] .

[ a                  basics:constant_function ;
  rdfs:domain        :MyLine_from_2007-03-14T11:00_to_12:00 ;
  rdfs:range         iso31:power ;
  rdfs:subPropertyOf myOnt:active_power ;
  basics:value_of_constant_function
                     [ a           iso31:power ;
                       scale:kW  [ basics:decimal  "15000" ] ] .

[ a                  basics:function ;
  rdfs:domain        :MyLine_from_2007-03-14T10:00_to_12:00 ;
  rdfs:range         iso31:power ;
  rdfs:subPropertyOf myOnt:active_power ;
  iso15926-x:function_mean
                     [ a           iso31:power ;
                       scale:kW  [ basics:decimal  "12500" ] ] .

• The distinction between a iso15926-2:possible_individual that exists for a finite period of time, and a iso15926-2:possible_individual that exists at an instant in time, to give possible_individual_during_period and possible_individual_at_instant.

• The distinction between a iso15926-2:possible_individual that exists within a region of space, and a iso15926-2:possible_individual that exists at a point in space, to give possible_individual_in_region and possible_individual_at_point_in_space.

• The distinction between a iso15926-2:period_in_time that is a finite period of time, and a iso15926-2:period_in_time that is a point in time, to give finite_period and instant.

• The distinction between a iso15926-2:spatial_location that is a finite region of space, and a iso15926-2:spatial_location that is a point in space, to give region_of_space and point_in_space.

• The relationship during between a possible_individual_during_period and a finite_period.

  NOTE The analogous spatial relationship geometry_basics:occupies_space is defined in ISO 15926-3.

• The relationship at_instant between a possible_individual_at_instant and a instant.

• The relationship at_point_in_space between a possible_individual_at_point_in_space and a point_in_space.

ISO 15926-3 defines the classes geometry_basics:time and geometry_basics:physical_space. There are many instances of geometry_basics:time and geometry_basics:physical_space depending upon the choice of frame of reference. Choices of particular relevance to this part of ISO 15926 are:

• wgs84_space that is defined by WGS84 (see Department of Defense, National Geophysical Agency (NGA) World Geodetic System 1984 (WGS 84)) and in which the Earth is more or less at rest. A point within wgs84_space can be identified by wgs84.

• tai_time that is International Atomic Time (TAI). A point within tai_time can be identified by UTC (see utc_iso8601).

This part of ISO 15926 defines the following properties of a function:

• function_maximum - the maximum value for each point in its domain;
• function_minimum - the minimum value for each point in its domain;
• function_mean - the mean value over all points in its domain;
• integral - the integral over its entire domain.

This part of ISO 15926 defines the property nominal_value for a basics:sub_metric_space. It gives a basics:metric_space_point which is close to, but not necessarily in, the basics:sub_metric_space, and which can be used to say roughly where the basics:sub_metric_space is.

An object is a possible_individual_during_period if and only if:

• it is a iso15926-2:possible_individual;
• it exists only throughout a finite_period.

-->
<owl:Class rdf:about="&iso15926-x;possible_individual_during_period">
 <rdfs:subClassOf rdf:resource="&iso15926-2;possible_individual"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#possible_individual_during_period"/>
</owl:Class>
<!--

An object is a possible_individual_at_instant if and only if:

• it is a iso15926-2:possible_individual;
• it exists only at an instant.

-->
<owl:Class rdf:about="&iso15926-x;possible_individual_at_instant">
 <rdfs:subClassOf rdf:resource="&iso15926-2;possible_individual"/>
 <owl:disjointWith rdf:resource="&iso15926-x;possible_individual_during_period"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#possible_individual_at_instant"/>
</owl:Class>
<!--

An object is a possible_individual_in_region if and only if:

• it is a iso15926-2:possible_individual;
• it exists only throughout a region_of_space.

-->
<owl:Class rdf:about="&iso15926-x;possible_individual_in_region">
 <rdfs:subClassOf rdf:resource="&iso15926-2;possible_individual"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#possible_individual_in_region"/>
</owl:Class>
<!--

An object is a possible_individual_at_point_in_space if and only if:

• it is a iso15926-2:possible_individual;
• it exists only at an point_in_space.

-->
<owl:Class rdf:about="&iso15926-x;possible_individual_at_point_in_space">
 <rdfs:subClassOf rdf:resource="&iso15926-2;possible_individual"/>
 <owl:disjointWith rdf:resource="&iso15926-x;possible_individual_in_region"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#possible_individual_at_point_in_space"/>
</owl:Class>
<!--

An object is a instant if and only if:

• it is a basics:structure_point;
• it is within a geometry_basics:time.

-->
<owl:Class rdf:about="&iso15926-x;instant">
 <owl:equivalentClass>
  <owl:Class>
   <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class rdf:about="&basics;structure_point"/>
    <owl:Restriction>
     <owl:onProperty rdf:resource="&basics;point_in_structure"/>
     <owl:allValuesFrom rdf:resource="&iso15926-x;time"/>
    </owl:Restriction>
   </owl:intersectionOf>
  </owl:Class>
 </owl:equivalentClass>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#instant"/>
</owl:Class>
<!--

An object is a point_in_space if and only if:

• it is a basics:structure_point;
• it is within a geometry_basics:physical_space.

-->
<owl:Class rdf:about="&iso15926-x;point_in_space">
 <owl:equivalentClass>
  <owl:Class>
   <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class rdf:about="&basics;structure_point"/>
    <owl:Restriction>
     <owl:onProperty rdf:resource="&basics;point_in_structure"/>
     <owl:allValuesFrom rdf:resource="&iso15926-x;physical_space"/>
    </owl:Restriction>
   </owl:intersectionOf>
  </owl:Class>
 </owl:equivalentClass>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#point_in_space"/>
</owl:Class>
<!--

An object is a finite_period if and only if:

• it is part a geometry_basics:time;
• it is a topology:directed_manifold_edge.

-->
<owl:Class rdf:about="&iso15926-x;finite_period">
 <owl:equivalentClass>
  <owl:Class>
   <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class rdf:resource="&topology;directed_manifold_edge"/>
    <owl:Restriction>
     <owl:onProperty rdf:resource="&basics;containing_structure_for_sub_structure"/>
     <owl:allValuesFrom rdf:resource="&geometry_basics;time"/>
    </owl:Restriction>
   </owl:intersectionOf>
  </owl:Class>
 </owl:equivalentClass>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#finite_period"/>
</owl:Class>
<!--

An object is a region_of_space if and only if:

• it is part a geometry_basics:time;
• it is a topology:manifold_3d.

-->
<owl:Class rdf:about="&iso15926-x;region_of_space">
 <owl:equivalentClass>
  <owl:Class>
   <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class rdf:resource="&topology;manifold_3d"/>
    <owl:Restriction>
     <owl:onProperty rdf:resource="&basics;containing_structure_for_sub_structure"/>
     <owl:allValuesFrom rdf:resource="&geometry_basics;physical_space"/>
    </owl:Restriction>
   </owl:intersectionOf>
  </owl:Class>
 </owl:equivalentClass>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#region_of_space"/>
</owl:Class>
<!--

An object is a during relationship if and only if:

• it is a basics:function from possible_individual_during_period to finite_period;
• it specifies that the possible_individual_during_period exists throughout the finite_period and does not exists outside the finite_period.

-->
<owl:FunctionalProperty rdf:about="&iso15926-x;during">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&iso15926-x;possible_individual_during_period"/>
 <rdfs:range rdf:resource="&iso15926-x;period"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#during"/>
</owl:FunctionalProperty>
<!--

An object is a at_instant relationship if and only if:

• it is a basics:function from possible_individual_at_instant to instant;
• it specifies that the possible_individual_at_instant exists at the instant and does not exists at any other instant.

-->
<owl:FunctionalProperty rdf:about="&iso15926-x;at_instant">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&iso15926-x;possible_individual_at_instant"/>
 <rdfs:range rdf:resource="&iso15926-x;instant"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#at_instant"/>
</owl:FunctionalProperty>
<!--

An object is a at_point_in_space relationship if and only if:

• it is a basics:function from possible_individual_at_point_in_space to point_in_space;
• it specifies that the possible_individual_at_point_in_space exists at the point_in_space and does not exists at any other point_in_space.

-->
<owl:FunctionalProperty rdf:about="&iso15926-x;at_point_in_space">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&iso15926-x;possible_individual_at_point_in_space"/>
 <rdfs:range rdf:resource="&iso15926-x;point_in_space"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#at_point_in_space"/>
</owl:FunctionalProperty>
<!--

The geometry_basics:time tai_time is the domain of the scale International Atomic Time (TAI).

-->
<owl:Class rdf:about="&iso15926-x;tai_time">
 <rdf:type rdf:resource="&geometry_basics;time"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#tai_time"/>
</owl:Class>
<!--

The geometry_basics:physical_space wgs84_space is the domain of the scale Department of Defense, National Geophysical Agency (NGA) World Geodetic System 1984 (WGS 84).

-->
<owl:Class rdf:about="&iso15926-x;wgs84_space">
 <rdf:type rdf:resource="&geometry_basics;physical_space"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#wgs84_space"/>
</owl:Class>
<!--

An object is an utc_iso8601 relationship if and only if:

• it is a basics:function from tai_time to the space of text strings for the representation of UTC defined by ISO 8601:2004;
• it identifies time points according to UTC.

An evaluation of utc_iso8601 identifies a point within tai_time and not a finite_period. This is true even if the text string could identify many different points.

-->
<owl:DatatypeProperty rdf:about="&iso15926-x;utc_iso8601">
 <rdfs:domain rdf:resource="&iso15926-x;tai_time"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#utc_iso8601"/>
</owl:DatatypeProperty>
<!--

An object is an utc_iec61850 relationship if and only if:

• it is a basics:function from tai_time to the space of lists for the representation of UTC defined by IEC 61850-7-2:2003;
• it identifies time points according to UTC.

The items in a member of the space of lists have the semantics:

1. integer: SecondOfCentury;
2. integer pair: FractionOfSecond (numerator followed by denominator);
3. Boolean: LeapSecondPending;
4. Boolean: LeapSecondOccured;
5. Boolean: LeapSecondNegative,

where the definitions of SecondOfCentury, FractionOfSecond, LeapSecondPending, LeapSecondOccured and LeapSecondNegative are given in IEC 61850-7-2:2003.

[ a                       iso15926-x:tai_time ;
  iso15926-x:utc_iec61850 ( [ basics:decimal "951537615" ]
                            ( [basics:decimal "5"] [basics:decimal "10"] )
                            iso15926-x:false
                            iso15926-x:false
                            iso15926-x:false
                          )
]

-->
<owl:ObjectProperty rdf:about="&iso15926-x;utc_iec61850">
 <rdfs:domain rdf:resource="&iso15926-x;tai_time"/>
 <rdfs:range rdf:resource="&rdf;List"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#utc_iec61850"/>
</owl:ObjectProperty>
<!--

An object is an wgs84 relationship if and only if:

• it is a basics:function from wgs84_space to basics:list_of_reals;
• it identifies points in space according to WGS84.

-->
<owl:FunctionalProperty rdf:about="&iso15926-x;wgs84">
 <rdfs:domain rdf:resource="&iso15926-x;wgs84_space"/>
 <rdfs:range rdf:resource="&rdf;List"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#wgs84"/>
</owl:FunctionalProperty>
<!--

An object is a function_mean relationship if and only if:

• it is a basics:mapping with domain basics:function;

• for a function f:X → Y, it evaluates to give the member of Y as follows:

  • as an integral:

    ∫X	f(x) dx
    ∫X	dx

  • as a sum:

    ∑x ∈X	f(x)
    ∑x ∈X	1

-->
<owl:ObjectProperty rdf:about="&iso15926-x;function_mean">
 <rdfs:domain rdf:resource="&basics;function"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#function_mean"/>
</owl:ObjectProperty>
<!--

An object is a function_maximum relationship if and only if:

• it is a basics:mapping with domain basics:function;
• for a function f:X → Y, it evaluates to give the member of Y that is the maximum of f(x) for x ∈ X.

-->
<owl:ObjectProperty rdf:about="&iso15926-x;function_maximum">
 <rdfs:domain rdf:resource="&basics;function"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#function_maximum"/>
</owl:ObjectProperty>
<!--

An object is a function_minimum relationship if and only if:

• it is a basics:mapping with domain basics:function;
• for a function f:X → Y, it evaluates to give the member of Y that is the minimum of f(x) for x ∈ X.

-->
<owl:ObjectProperty rdf:about="&iso15926-x;function_minimum">
 <rdfs:domain rdf:resource="&basics;function"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#function_minimum"/>
</owl:ObjectProperty>
<!--

An object is a integral relationship if and only if:

• it is a basics:mapping with domain basics:function;

• for a function f:X → Y, it evaluates to give the member of Y as follows:

  ∫X

  f(x) dx

-->
<owl:ObjectProperty rdf:about="&iso15926-x;integral">
 <rdfs:domain rdf:resource="&basics;function"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#integral"/>
</owl:ObjectProperty>
<!--

An object is a nominal_value relationship if and only if:

• it is a basics:mapping between basics:sub_structure and basics:structure_point;
• the basics:structure_point ia an approximate location for the basics:sub_structure.

-->
<owl:ObjectProperty rdf:about="&iso15926-x;nominal_value">
 <rdfs:domain rdf:resource="&basics;sub_structure"/>
 <rdfs:range rdf:resource="&basics;structure_point"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#nominal_value"/>
</owl:ObjectProperty>
<!--

An object is a member of true if and only if:

• it is a statement;
• it is true.

-->
<owl:Class rdf:about="&iso15926-x;true">
 <rdfs:subClassOf rdf:resource="&rdf;Statement"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#true"/>
</owl:Class>
<!--

An object is a member of false if and only if:

• it is a statement;
• it is not true.

-->
<owl:Class rdf:about="&iso15926-x;false">
 <rdfs:subClassOf rdf:resource="&rdf;Statement"/>
 <owl:disjointWith rdf:resource="&iso15926-x;true"/>
 <rdfs:isDefinedBy rdf:resource="&iso15926-x-doc;/temporal_part_and_time.htm#false"/>
</owl:Class>
<!--

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