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   <!ENTITY basics           "http://www.somewhere#">
   <!ENTITY topology         "http://www.somewhere#">
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 &lt;title&gt;S-TEN D2.1: Temporal part and time&lt;/title&gt;
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&lt;a name="temporal_part_and_time"/&gt;
&lt;h2&gt;4 Temporal part and time&lt;/h2&gt;

&lt;a name="what_is_a_temporal_part"/&gt;
&lt;h3&gt;4.1 What is a temporal part&lt;/h3&gt;
&lt;p&gt;A temporal part is all of a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; for a part of its life.
A temporal part is:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;an instant in the life of a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;a interval in the life of a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;a combination of one or more instants and intervals.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;A relationship with a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; which exists for only a part of
its life, is assigned to the appropriate temporal part.&lt;/p&gt;

&lt;div class="note"&gt;
&lt;p&gt;NOTE 1 The assignment of relationships to temporal parts is the way in which time
variation is addressed by the S-TEN ontology. This approach is sometimes refered to
as " &lt;a href="http://coli.lili.uni-bielefeld.de/~felix/lehre/ws04_05/ontologischeRessourcen/addLiterature/farrar-und-bateman04.pdf"&gt;4D modelling&lt;/a&gt;". This approach is used
in &lt;a href="http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema.html"&gt;ISO 15926-2&lt;/a&gt;.&lt;/p&gt;
&lt;/div&gt;

&lt;div class="note"&gt;
&lt;p&gt;NOTE 2 Some relationships are with instants rather than periods. Such
relationships can be considered as a
a function over a space of temporal instants. This is discussed in
Section &lt;a href="#an_approach_to_property_variation"&gt;4.4&lt;/a&gt;.&lt;/p&gt;
&lt;/div&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE Consider a network "my_network" with component instances of &lt;a href="physical_things.htm#facility"&gt;&lt;b&gt;sten:facility&lt;/b&gt;&lt;/a&gt; "X-101" and
"X-102". X-102 is added to the network at T&lt;sub&gt;2&lt;/sub&gt;,
and X-101 is removed at T&lt;sub&gt;3&lt;/sub&gt;.&lt;/p&gt;

&lt;p&gt;Instances of &lt;a href="physical_things.htm#physical_asset"&gt;&lt;b&gt;sten:physical_asset&lt;/b&gt;&lt;/a&gt; are installed to be the facilities as follows:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;X-101 is asset 98-1234 from before T&lt;sub&gt;0&lt;/sub&gt; until T&lt;sub&gt;1&lt;/sub&gt;.
At T&lt;sub&gt;1&lt;/sub&gt;, 98-1234 is sent for refurbishment, and 03-2345 is taken from the stores and installed
until the end of the life of X-101.&lt;/li&gt;
&lt;li&gt;X-102 is asset 99-5678 from the beginning of its life until after T&lt;sub&gt;4&lt;/sub&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;This information is shown diagramatically in
Figure &lt;a href="#temporal_parts_and_installation_fig"&gt;3&lt;/a&gt;.&lt;/p&gt;

&lt;div align="center"&gt;
&lt;a name="temporal_parts_and_installation_fig"/&gt;
&lt;img src="../images/temporal_parts_and_installation.gif"
     alt="Temporal parts and installation"/&gt;
&lt;p class="caption"&gt;&lt;b&gt;Figure 3: Temporal parts and installation&lt;/b&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p&gt;The recording of this information using temporal parts is as follows:&lt;/p&gt;

&lt;p&gt;&lt;b&gt;components of the network:&lt;/b&gt;&lt;/p&gt;
&lt;pre&gt;
:my_network  a               sten:facility ;
             a               topology:directed_manifold_edge ;
             topology:end_1  [ sten:at_time [ sten:before :T0 ] ] ;
             topology:end_2  [ sten:at_time [ sten:after  :T4 ] ] .

:X-101       a               sten:facility ;
             a               topology:directed_manifold_edge ;
             topology:end_1  [ sten:at_time [ sten:before :T0 ] ] ;
             topology:end_2  [ sten:at_time :T3 ] ] .

:X-102       a               sten:facility ;
             a               topology:directed_manifold_edge ;
             topology:end_1  [ sten:at_time :T2 ] ;
             topology:end_2  [ sten:at_time [ sten:after :T4 ] ] .

[ sten:temporal_part_of :my_network ;
  topology:end_1        [ sten:at_time [ sten:before :T0 ] ] ;
  topology:end_2        [ sten:at_time :T3 ]
]
             sten:has_component [ sten:temporal_part_of :X_101 ] .

[ sten:temporal_part_of :my_network ;
  topology:end_1        [ sten:at_time :T2 ] ;
  topology:end_2        [ sten:at_time [ sten:after :T4 ] ]
]
             sten:has_component [ sten:temporal_part_of :X_102 ] .
&lt;/pre&gt;

&lt;p&gt;&lt;b&gt;installed assets:&lt;/b&gt;&lt;/p&gt;
&lt;pre&gt;
:98-1234     a               sten:physical_asset ;
             a               topology:directed_manifold_edge ;
             topology:end_1  [ sten:at_time [ sten:before :T0 ] ] ;
             topology:end_2  [ sten:at_time [ sten:after  :T4 ] ] .

:99-5678     a               sten:physical_asset ;
             a               topology:directed_manifold_edge ;
             topology:end_1  [ sten:at_time [ sten:before :T0 ] ] ;
             topology:end_2  [ sten:at_time [ sten:after  :T4 ] ] .

:03-2345     a               sten:physical_asset ;
             a               topology:directed_manifold_edge ;
             topology:end_1  [ sten:at_time [ sten:before :T0 ] ] ;
             topology:end_2  [ sten:at_time [ sten:after  :T4 ] ] .

[ sten:temporal_part_of :X-101 ;
  topology:end_1      [ sten:at_time [ sten:before :T0 ] ] ;
  topology:end_2      [ sten:at_time :T1 ]
]
             =  [ sten:temporal_part_of :98-1234 ] .

[ sten:temporal_part_of :X-101 ;
  topology:end_1      [ sten:at_time :T1 ] ] ;
  topology:end_2      [ sten:at_time :T3 ]
]
             =  [ sten:temporal_part_of :03-2345 ] .

[ sten:temporal_part_of :X-102 ;
  topology:end_1      [ sten:at_time :T2 ] ;
  topology:end_2      [ sten:at_time [ sten:after :T4 ] ]
]
             =  [ sten:temporal_part_of :99-5678 ] .
&lt;/pre&gt;

&lt;p&gt;The installation relationship between a temporal part of a
&lt;a href="physical_things.htm#facility"&gt;&lt;b&gt;sten:facility&lt;/b&gt;&lt;/a&gt; and a temporal part of a &lt;a href="physical_things.htm#physical_asset"&gt;&lt;b&gt;sten:physical_asset&lt;/b&gt;&lt;/a&gt; is expressed as an &lt;b&gt;owl:sameAs&lt;/b&gt;
relationship , which
is abbreviated to "=" in N3. On one side of the "=", the beginning and end times of the
temporal part are stated. They are not stated on the other side, because "=" requires
that they are the same.&lt;/p&gt;

&lt;p&gt;If the temporal parts are named object which are defined separately, then it may be
better to specify the start and end times for each. This would enable software to
check that the "=" is valid. This is shown as follows.&lt;/p&gt;

&lt;pre&gt;
:X-101_T0_T1   sten:temporal_part_of :X-101 ;
               topology:end_1        [ sten:at_time [ sten:before :T0 ] ] ;
               topology:end_2        [ sten:at_time :T1 ] .

:98-1234_T0_T1 sten:temporal_part_of :X-101 ;
               topology:end_1        [ sten:at_time [ sten:before :T0 ] ] ;
               topology:end_2        [ sten:at_time :T1 ] .

:X-101_T0_T1   =  :98-1234_T0_T1 .
&lt;/pre&gt;

&lt;/div&gt;

&lt;div class="note"&gt;
&lt;p&gt;NOTE 3  The assumption that a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; is a
&lt;b&gt;topology:directed_manifold_edge&lt;/b&gt; is convenient for this example. The
assumption enables a temporal part to be defined by the properties
&lt;b&gt;topology:end_1&lt;/b&gt; and &lt;b&gt;topology:end_2&lt;/b&gt;. Each point within the 1D manifold
is a
&lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt;.
&lt;/p&gt;

&lt;p&gt;The assumption of a structure for a temporal part, such as
&lt;b&gt;topology:directed_manifold_edge&lt;/b&gt;, is discussed in Section
&lt;a href="physical_things.htm#physical_thing_and_structure"&gt;Physical thing and structure&lt;/a&gt;.
The ontology used to defined the structure is contained in ISO/TS 15926-3.
This standard has passed its CD ballot, but has not yet been published. Until
publication, the S-TEN project is using a pre-publication OWL/XML serialisation of the
ontology which is contained in
&lt;a href="http://www.s-ten.eu/iso15926-3_pre-publication/iso_ts_15926-3.htm"&gt;&lt;code&gt;http://www.s-ten.eu/iso15926-3_pre-publication/iso_ts_15926-3.htm&lt;/code&gt;&lt;/a&gt;. After publication,
the OWL/XML serialisation will be downloadable from an ISO website.&lt;/p&gt;

&lt;p&gt;Many different possible assumptions can be made about the structure of a
&lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;. These include:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;&lt;p&gt;A 4D manifold, within which each point is a material point at an
instant.&lt;/p&gt;&lt;/li&gt;

&lt;li&gt;&lt;p&gt;A 2D manifold, within which each point is a cross-section at an
instant. This approach can be used to represent a property of a beam as it
changes with time.&lt;/p&gt;&lt;/li&gt;

&lt;li&gt;&lt;p&gt;A 1D manifold, within which each point is a "temporal plane". The example
above is a special case of this in which the temporal plane corresponds to a
&lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt;. For some special applications, such as
fluid flow through rotating machinery, it is also possible to consider
"inclined temporal planes". This is shown in
Figure &lt;a href="#vertical_and_inclined_temporal_planes_fig"&gt;4&lt;/a&gt;.&lt;/p&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;div align="center"&gt;
&lt;a name="vertical_and_inclined_temporal_planes_fig"/&gt;
&lt;img src="../images/vertical_and_inclined_temporal_planes.gif"
     alt="'Vertical' and 'inclined' temporal planes"/&gt;
&lt;p class="caption"&gt;&lt;b&gt;Figure 4: "Vertical" and "inclined" temporal planes&lt;/b&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;/div&gt;

&lt;a name="use_of_temporal_part"/&gt;
&lt;h3&gt;4,2 Use of temporal part&lt;/h3&gt;

&lt;p&gt;Many types of relationship are necessarily between simultaneous temporal parts.&lt;/p&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE 1 If Janet has a married_to relationship with John, then the relationship
is between simultaneous temporal parts of each. This is shown as follows:&lt;/p&gt;
&lt;pre&gt;
[ sten:temporal_part_of :Janet ;
  sten:during  [ topology:end_1 [ sten:utc_iso8601 "2007-03-10" ]  ]
]
    :married_to  [ sten:temporal_part_of :John ] .
&lt;/pre&gt;

&lt;p&gt;The temporal part of Janet, that is married to John, has a beginnning on
2007-03-10, and an unspecified end. The temporal part of John, that is married to
Janet, exists during the same &lt;a href="#period"&gt;&lt;b&gt;sten:period&lt;/b&gt;&lt;/a&gt;.&lt;/p&gt;
&lt;/div&gt;

&lt;p&gt;If a relationship is necessarily between simultaneous temporal parts, then the
&lt;a href="#period"&gt;&lt;b&gt;sten:period&lt;/b&gt;&lt;/a&gt; for one need not be specified. That a
type of relationship is necessarily between simultaneous temporal parts is
specified by classification as a
&lt;a href="#simultaneous_mapping"&gt;&lt;b&gt;sten:simultaneous_mapping&lt;/b&gt;&lt;/a&gt;.&lt;/p&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE 2: Information about &lt;b&gt;married_to&lt;/b&gt; is as follows:&lt;/p&gt;
&lt;pre&gt;
<owl:FunctionalProperty rdf:about="#married_to">
 <rdf:type rdf:resource="sten;simultaneous_mapping"/>
 <rdfs:domain>
  <owl:Restriction>
   <owl:onProperty rdf:resource="sten;temporal_part_of"/>
   <owl:someValuesFrom rdf:resource="#Person"/>
  </owl:Restriction>
 </rdfs:domain>
 <rdfs:range>
  <owl:Restriction>
   <owl:onProperty rdf:resource="sten;temporal_part_of"/>
   <owl:someValuesFrom rdf:resource="#Person"/>
  </owl:Restriction>
 </rdfs:range>
</owl:FunctionalProperty>
&lt;/pre&gt;

&lt;p&gt;The domain and range of &lt;b&gt;married_to&lt;/b&gt; is not &lt;b&gt;Person&lt;/b&gt;, but
temporal part of a &lt;b&gt;Person&lt;/b&gt;.&lt;/p&gt;
&lt;/div&gt;

&lt;p&gt;An &lt;a href="physical_things.htm#activity"&gt;&lt;b&gt;sten:activity&lt;/b&gt;&lt;/a&gt; is specifically
defined to record relationships between
instances of
&lt;a href="physical_things.htm#persistent_object"&gt;&lt;b&gt;sten:persistent_object&lt;/b&gt;&lt;/a&gt;.
Hence it is a
&lt;a href="physical_things.htm#persistent_object"&gt;&lt;b&gt;sten:persistent_object&lt;/b&gt;&lt;/a&gt; which
has a role in an
&lt;a href="physical_things.htm#activity"&gt;&lt;b&gt;sten:activity&lt;/b&gt;&lt;/a&gt;
rather than a temporal part of it.&lt;/p&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE 3 If Janet has a married_to relationship with John, then there is
a marriage activity in which they both participate as spouse.
This is shown as follows:&lt;/p&gt;

&lt;pre&gt;
[ a            :marriage ;
  sten:during  [ topology:end_1 [ sten:utc_iso8601 "2007-03-10" ]  ]
]
  :spouse :Janet ;
  :spouse :John  .
&lt;/pre&gt;
&lt;/div&gt;

&lt;a name="ontology_for_temporal_part"/&gt;
&lt;h3&gt;4.3 Ontology for temporal part&lt;/h3&gt;

&lt;a name="has_temporal_part"/&gt;
&lt;h3&gt;4.3.1 has_temporal_part&lt;/h3&gt;
&lt;p&gt;An object is an &lt;a href="#has_temporal_part"&gt;&lt;b&gt;sten:has_temporal_part&lt;/b&gt;&lt;/a&gt;
relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;a href="physical_things.htm#has_part"&gt;&lt;b&gt;sten:has_part&lt;/b&gt;&lt;/a&gt; relationship;&lt;/li&gt;
&lt;li&gt;the part is all of the whole for a &lt;a href="#part_of_time"&gt;&lt;b&gt;sten:part_of_time&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;If the object in the domain is a &lt;b&gt;basics:structure&lt;/b&gt;, then the
object in the range consists of one or more members of
&lt;b&gt;basics:sub_structure&lt;/b&gt; or &lt;b&gt;basics:structure_point&lt;/b&gt;.&lt;/p&gt;

&lt;p&gt;If the object in the domain is a &lt;b&gt;topology:directed_manifold_edge&lt;/b&gt;,
then the object in the range consists of one or more members of
&lt;b&gt;topology:directed_manifold_edge&lt;/b&gt; or &lt;b&gt;basics:structure_point&lt;/b&gt;.&lt;/p&gt;

&lt;p&gt;The relationship &lt;a href="#temporal_part_of"&gt;&lt;b&gt;sten:has_temporal_part&lt;/b&gt;&lt;/a&gt;
includes equality. Hence a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; has a
&lt;a href="#temporal_part_of"&gt;&lt;b&gt;sten:temporal_part_of&lt;/b&gt;&lt;/a&gt; relationship with
itself.&lt;/p&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
<owl:TransitiveProperty rdf:about="&sten;has_temporal_part">
 <rdfs:subPropertyOf rdf:resource="&sten;has_part"/>
 <rdfs:domain rdf:resource="&sten;classical_object"/>
 <rdfs:rangerdf:resource="&sten;physical_thing"/>
 <owl:sameAs rdf:resource="&sumo;temporal_part/">
 <rdfs:subPropertyOf rdf:resource="&iso15926-2;temporal_whole_part.part"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#has_temporal_part"/>
</owl:TransitiveProperty>
&lt;/pre&gt;

&lt;a name="temporal_part_of"/&gt;
&lt;h3&gt;4.3.2 temporal_part_of&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#temporal_part_of"&gt;&lt;b&gt;sten:temporal_part_of&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;a href="physical_things.htm#part_of"&gt;&lt;b&gt;sten:part_of&lt;/b&gt;&lt;/a&gt; relationship;&lt;/li&gt;
&lt;li&gt;it is the inverse of &lt;a href="#has_temporal_part"&gt;&lt;b&gt;sten:has_temporal_part&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;If the object in the range is a &lt;b&gt;basics:structure&lt;/b&gt;, then the
object in the domain consists of one or more members of
&lt;b&gt;basics:sub_structure&lt;/b&gt; or &lt;b&gt;basics:structure_point&lt;/b&gt;.&lt;/p&gt;

&lt;p&gt;If the object in the range is a &lt;b&gt;topology:directed_manifold_edge&lt;/b&gt;,
then the object in the domain consists of one or more members of
&lt;b&gt;topology:directed_manifold_edge&lt;/b&gt; or &lt;b&gt;basics:structure_point&lt;/b&gt;.&lt;/p&gt;

&lt;p&gt;The relationship &lt;a href="#temporal_part_of"&gt;&lt;b&gt;sten:temporal_part_of&lt;/b&gt;&lt;/a&gt;
includes equality. Hence a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; has a
&lt;a href="#temporal_part_of"&gt;&lt;b&gt;sten:temporal_part_of&lt;/b&gt;&lt;/a&gt; relationship with
itself.&lt;/p&gt;

&lt;div class="note"&gt;
&lt;p&gt;NOTE &lt;a href="#temporal_part_of"&gt;&lt;b&gt;sten:temporal_part_of&lt;/b&gt;&lt;/a&gt; is
approximately equivalent to &lt;b&gt;iso15926-2:temporal_whole_part&lt;/b&gt;. A difference is that a
&lt;b&gt;temporal_whole_part&lt;/b&gt; can relate instances of &lt;b&gt;iso15926-2:possible_individual&lt;/b&gt;,
where &lt;b&gt;iso15926-2:possible_individual&lt;/b&gt; is equivalent to
&lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt;. In the STEN ontology a temporal part relationship
is only valid for a whole &lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt;
which evolves through time, i.e. a
&lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;In the OWL ontology for ISO 15926-2, the bi-directional entity
&lt;b&gt;iso15926-2:temporal_whole_part&lt;/b&gt; corresponds to the two
relationships &lt;b&gt;iso15926-2:temporal_whole_part.part&lt;/b&gt; and
&lt;b&gt;iso15926-2:temporal_whole_part.whole&lt;/b&gt;.&lt;/p&gt;
&lt;/div&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:TransitiveProperty rdf:about="&sten;temporal_part_of">
 <rdfs:subPropertyOf rdf:resource="&sten;part_of"/>
 <owl:inverseOf rdf:resource="&sten;has_temporal_part"/>
 <rdfs:domain rdf:resource="&sten;physical_thing"/>
 <rdfs:range rdf:resource="&sten;classical_object"/>
 <rdfs:subPropertyOf rdf:resource="&iso15926-2;temporal_whole_part.whole"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#temporal_part_of"/>
</owl:TransitiveProperty>
<!--
&lt;/pre&gt;

&lt;a name="an_approach_to_time"/&gt;
&lt;h3&gt;4.4 An approach to time&lt;/h3&gt;

&lt;p&gt;In this ontology, the universe is regarded as a 1D manifold of 3D manifolds, where there is a
frame of reference such that in each 3D manifold all the points are
simultaneous.&lt;/p&gt;

&lt;p&gt;A "time" is such a 1D manifold. There are many possible times, of which one is
&lt;a href="http://www.bipm.org/en/scientific/tai/tai.html"&gt;International Atomic Time (TAI)&lt;/a&gt;
experienced by a network of clocks on the surface of the earth. A point in TAI
can be identified using
&lt;a href="http://www.bipm.org/en/scientific/tai/time_server.html"&gt;Coordinated Universal Time (UTC)&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;The universe (in the neighbourhood of a set of clocks) is a
&lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;, which has temporal parts. Any
smaller &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; can be regarded as a component of the
appropriate temporal part of the universe. Similarly a smaller
&lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt; can be regarded as a component of the
appropriate member of a "time". The two component relationships are given
special names as follows:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="#during"&gt;&lt;b&gt;sten:during&lt;/b&gt;&lt;/a&gt; which specifies that a
&lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; exists during a &lt;a href="#part_of_time"&gt;&lt;b&gt;sten:part_of_time&lt;/b&gt;&lt;/a&gt;; and&lt;/li&gt;
&lt;li&gt;&lt;a href="#at_time"&gt;&lt;b&gt;sten:at_time&lt;/b&gt;&lt;/a&gt; which specifies that a
&lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt; exists at a time.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The two component relationships can be used to specify the duration of
a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; in two ways, as follows:&lt;/p&gt;

&lt;p&gt;&lt;b&gt;end points of &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;&lt;/b&gt;&lt;/p&gt;
&lt;pre&gt;
:my_classical_object
     a               sten:classical_object ;
     a               topology:directed_manifold_edge ;
     topology:end_1  [ sten:at_time [ sten:utc_iso8601 "2007-02-10T11:30" ] ] ;
     topology:end_2  [ sten:at_time [ sten:utc_iso8601 "2007-02-10T15:45" ] ] .
&lt;/pre&gt;

&lt;p&gt;&lt;b&gt;end points of time interval&lt;/b&gt;&lt;/p&gt;
&lt;pre&gt;
:my_classical_object
     a               sten:classical_object ;
     a               topology:directed_manifold_edge ;
     sten:during     [ topology:end_1  [ sten:utc_iso8601 "2007-02-10T11:30" ] ;
                       topology:end_2  [ sten:utc_iso8601 "2007-02-10T15:45" ]
                     ] .
&lt;/pre&gt;

&lt;a name="time_ontology"/&gt;
&lt;h3&gt;4.5 Time ontology&lt;/h3&gt;

&lt;a name="time"/&gt;
&lt;h3&gt;4.5.1 time&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#time"&gt;&lt;b&gt;sten:time&lt;/b&gt;&lt;/a&gt; if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a partition of a part of the universe;&lt;/li&gt;
&lt;li&gt;there is an observer for which each item within the partition
consists of things which are simultaneous.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;time">
 <rdfs:subClassOf rdf:resource="&sten;classical_object"/>
 <rdfs:subClassOf rdf:resource="&topology;directed_manifold_edge"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#time"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="instant"/&gt;
&lt;h3&gt;4.5.2 instant&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#instant"&gt;&lt;b&gt;sten:instant&lt;/b&gt;&lt;/a&gt; if and only
if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:structure_point&lt;/b&gt;
within a &lt;a href="#time"&gt;&lt;b&gt;sten:time&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;instant">
 <owl:equivalentClass>
  <owl:Restriction>
   <owl:onProperty rdf:resource="&basics;point_has_containing_structure"/>
   <owl:allValuesFrom rdf:resource="&sten;time"/>
  </owl:Restriction>
 </owl:equivalentClass>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#instant"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="part_of_time"/&gt;
&lt;h3&gt;4.5.3 part_of_time&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#part_of_time"&gt;&lt;b&gt;sten:part_of_time&lt;/b&gt;&lt;/a&gt; if and only
if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it has a &lt;a href="#temporal_part_of"&gt;&lt;b&gt;sten:temporal_part_of&lt;/b&gt;&lt;/a&gt;
relationship with a &lt;a href="#time"&gt;&lt;b&gt;sten:time&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;part_of_time">
 <owl:equivalentClass>
  <owl:Restriction>
   <owl:onProperty rdf:resource="&sten;temporal_part_of"/>
   <owl:allValuesFrom rdf:resource="&sten;time"/>
  </owl:Restriction>
 </owl:equivalentClass>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#part_of_time"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="period"/&gt;
&lt;h3&gt;4.5.4 period&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#period"&gt;&lt;b&gt;sten:period&lt;/b&gt;&lt;/a&gt; if and only
if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;a href="#part_of_time"&gt;&lt;b&gt;sten:part_of_time&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it is a &lt;b&gt;topology:directed_manifold_edge&lt;/b&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;part_of_time">
 <owl:equivalentClass>
  <owl:Class>
   <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class rdf:resource="&sten;part_of_time"/>
    <owl:Class rdf:resource="&topology;directed_manifold_edge"/>
   </owl:intersectionOf>
  </owl:Class>
 </owl:equivalentClass>
 <owl:sameAs rdf:resource="&iso15926-2;period_in_time"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#period"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="tai_time"/&gt;
&lt;h3&gt;4.5.5 tai_time&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#tai_time"&gt;&lt;b&gt;sten:tai_time&lt;/b&gt;&lt;/a&gt; if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;a href="#time"&gt;&lt;b&gt;sten:time&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it is the domain of the scale
&lt;a href="http://www.bipm.org/en/scientific/tai/tai.html"&gt;International Atomic Time (TAI)&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="note"&gt;
&lt;p&gt;NOTE This time is also the domain of the
&lt;a href="http://www.bipm.org/en/scientific/tai/time_server.html"&gt;UTC&lt;/a&gt; scale.
The UTC scale is defined with respect to the TAI scale.&lt;/p&gt;
&lt;/div&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&bipm;tai_time">
 <rdf:type rdf:resource="&sten;time"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#tai_time"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="during"/&gt;
&lt;h3&gt;4.5.6 during&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#during"&gt;&lt;b&gt;sten:during&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; from &lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt;
to &lt;a href="#part_of_time"&gt;&lt;b&gt;sten:part_of_time&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it specifies that the &lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt;
exists throughout the &lt;a href="#part_of_time"&gt;&lt;b&gt;sten:part_of_time&lt;/b&gt;&lt;/a&gt; and does not
exists outside the &lt;a href="#part_of_time"&gt;&lt;b&gt;sten:part_of_time&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:FunctionalProperty rdf:about="&sten;during">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&sten;physical_thing"/>
 <rdfs:range rdf:resource="&sten;part_of_time"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#during"/>
</owl:FunctionalProperty>
<!--
&lt;/pre&gt;

&lt;a name="at_time"/&gt;
&lt;h3&gt;4.5.7 at_time&lt;/h3&gt;
&lt;p&gt;An object is an &lt;a href="#at_time"&gt;&lt;b&gt;sten:at_time&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; from
&lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt;
to &lt;a href="#instant"&gt;&lt;b&gt;sten:instant&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it specifies that the &lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt; exists
at the &lt;a href="#instant"&gt;&lt;b&gt;sten:instant&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:FunctionalProperty rdf:about="&sten;at_time">
 <rdfs:domain rdf:resource="&sten;classical_object_at_instant"/>
 <rdfs:range rdf:resource="&sten;instant"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#at_time"/>
</owl:FunctionalProperty>
<!--
&lt;/pre&gt;

&lt;a name="before"/&gt;
&lt;h3&gt;4.5.8 before&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#before"&gt;&lt;b&gt;sten:before&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:mapping&lt;/b&gt; with domain and range &lt;a href="#instant"&gt;&lt;b&gt;sten:instant&lt;/b&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;it specifies that the domain object comes before the range object.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The relationship &lt;a href="#before"&gt;&lt;b&gt;sten:before&lt;/b&gt;&lt;/a&gt; is a specialisation of the relationship
&lt;a href="physical_things.htm#less_than"&gt;&lt;b&gt;sten:less_than&lt;/b&gt;&lt;/a&gt; for use with &lt;a href="#time"&gt;&lt;b&gt;sten:time&lt;/b&gt;&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:ObjectProperty rdf:about="&sten;before">
 <rdf:type rdf:resource="&basics;mapping"/>
 <rdfs:domain rdf:resource="&sten;instant"/>
 <rdfs:range rdf:resource="&sten;instant"/>
 <rdfs:subPropertyOf rdf:resource="&sten;less_than"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#before"/>
</owl:ObjectProperty>
<!--
&lt;/pre&gt;

&lt;a name="after"/&gt;
&lt;h3&gt;4.5.9 after&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#after"&gt;&lt;b&gt;sten:after&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:mapping&lt;/b&gt; with domain and range &lt;a href="#instant"&gt;&lt;b&gt;sten:instant&lt;/b&gt;&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;it specifies that the domain object comes after the range object.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The relationship &lt;a href="#after"&gt;&lt;b&gt;sten:after&lt;/b&gt;&lt;/a&gt; is a specialisation of the relationship
&lt;a href="physical_things.htm#greater_than"&gt;&lt;b&gt;sten:greater_than&lt;/b&gt;&lt;/a&gt; for use with &lt;a href="#time"&gt;&lt;b&gt;sten:time&lt;/b&gt;&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:ObjectProperty rdf:about="&sten;after">
 <rdf:type rdf:resource="&basics;mapping"/>
 <rdfs:domain rdf:resource="&sten;instant"/>
 <rdfs:range rdf:resource="&sten;instant"/>
 <rdfs:subPropertyOf rdf:resource="&sten;greater_than"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#after"/>
</owl:ObjectProperty>
<!--
&lt;/pre&gt;

&lt;a name="utc_iso8601"/&gt;
&lt;h3&gt;4.5.10 utc_iso8601&lt;/h3&gt;
&lt;p&gt;An object is an &lt;a href="#utc_iso8601"&gt;&lt;b&gt;sten:utc_iso8601&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; from
&lt;a href="#tai_time"&gt;&lt;b&gt;sten:tai_time&lt;/b&gt;&lt;/a&gt; to the space of text strings for the representation of
&lt;a href="http://www.bipm.org/en/scientific/tai/time_server.html"&gt;UTC&lt;/a&gt; defined by
&lt;a href="http://isotc.iso.org/livelink/livelink/4021199/ISO_8601_2004_E.zip?func=doc.Fetch&nodeid=4021199"&gt;ISO 8601:1988&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it identifies time points according to UTC.&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="note"&gt;
&lt;p&gt;NOTE An evaluation of &lt;a href="#utc_iso8601"&gt;&lt;b&gt;sten:utc_iso8601&lt;/b&gt;&lt;/a&gt; identifies a point within &lt;a href="#tai_time"&gt;&lt;b&gt;sten:tai_time&lt;/b&gt;&lt;/a&gt;
and not a &lt;a href="#period"&gt;&lt;b&gt;sten:period&lt;/b&gt;&lt;/a&gt;. This is true even if the text string could
identify many different points. For example the text string "2007-03-14" could
identify any point within the day.&lt;/p&gt;

&lt;p&gt;By analogy, the use of "Janet" in the statement "Janet loves Fred Bloggs" identifies
one person, even though there are many people called "Janet".&lt;/p&gt;
&lt;/div&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:DatatypeProperty rdf:about="&sten;utc_iso8601">
 <rdfs:domain rdf:resource="&sten;tai_time"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#utc_iso8601"/>
</owl:DatatypeProperty>
<!--
&lt;/pre&gt;

&lt;a name="utc_iec61850"/&gt;
&lt;h3&gt;4.5.11 utc_iec61850&lt;/h3&gt;
&lt;p&gt;An object is an &lt;a href="#utc_iec61850"&gt;&lt;b&gt;sten:utc_iec61850&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; from
&lt;a href="#tai_time"&gt;&lt;b&gt;sten:tai_time&lt;/b&gt;&lt;/a&gt; to the space of lists for the representation of
&lt;a href="http://www.bipm.org/en/scientific/tai/time_server.html"&gt;UTC&lt;/a&gt; defined by
&lt;a href="http://webstore.iec.ch/preview/info_iec61850-7-2%7Bed1.0%7Den.pdf"&gt;IEC 61850-7-2:2003&lt;/a&gt;
&lt;font size="-1"&gt;(This link is to the first few pages of the standard only.
The remainder has to be purchased from IEC)&lt;/font&gt;;&lt;/li&gt;
&lt;li&gt;it identifies time points according to UTC.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The items in a member of the space of lists have the semantics:&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;integer: SecondOfCentury;&lt;/li&gt;
&lt;li&gt;integer pair: FractionOfSecond;&lt;/li&gt;
&lt;li&gt;Boolean: LeapSecondPending;&lt;/li&gt;
&lt;li&gt;Boolean: LeapSecondOccured;&lt;/li&gt;
&lt;li&gt;Boolean: LeapSecondNegative,&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;where the definitions of SecondOfCentury, FractionOfSecond,
LeapSecondPending, LeapSecondOccured and LeapSecondNegative are given in
IEC 61850-7-2:2003.&lt;/p&gt;

&lt;p&gt;The representation of the items in the list within a serialisation of OWL is
as follows:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;integer: encoded using &lt;b&gt;basics:decimal&lt;/b&gt;;&lt;/li&gt;
&lt;li&gt;integer pair: the first is the numerator and the second is the denominator, and
each is encoded using &lt;b&gt;basics:decimal&lt;/b&gt;;
the numerator and the second ;&lt;/li&gt;
&lt;li&gt;Boolean: encoded using &lt;b&gt;sten:boolean&lt;/b&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE The time half a second after 2000-03-26T04:00:15 is represented as
follows:&lt;/p&gt;

&lt;pre&gt;
[ a                 sten:tai_time
  sten:utc_iec61850 ( [ basics:decimal "951537615" ]
                      ( [basics:decimal "5"] [basics:decimal "10"] )
                      [ sten:boolean "F" ]
                      [ sten:boolean "F" ]
                      [ sten:boolean "F" ]
                    )
]
&lt;/pre&gt;
&lt;/div&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:DatatypeProperty rdf:about="&sten;utc_iso8601">
 <rdfs:domain rdf:resource="&sten;tai_time"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#utc_iso8601"/>
</owl:DatatypeProperty>
<!--
&lt;/pre&gt;

&lt;a name="simultaneous_mapping"/&gt;
&lt;h3&gt;4.5.12 simultaneous_mapping&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#simultaneous_mapping"&gt;&lt;b&gt;sten:simultaneous_mapping&lt;/b&gt;&lt;/a&gt; if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;owl:ObjectProperty&lt;/b&gt;;&lt;/li&gt;
&lt;li&gt;each object in the domain maps to an object in the range which exists during
the same &lt;a href="#period"&gt;&lt;b&gt;sten:period&lt;/b&gt;&lt;/a&gt;
or at the same &lt;a href="#instant"&gt;&lt;b&gt;sten:instant&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;simultaneous_mapping">
 <rdfs:subClassOf rdf:resource="&owl;ObjectProperty"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#simultaneous_mapping"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="an_approach_to_property_variation"/&gt;
&lt;h3&gt;4.6 An approach to property variation&lt;/h3&gt;

&lt;p&gt;Some properties are possessed by a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; and others
are possessed by a &lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt;.&lt;/p&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE 1 Consider the transmission line "my_line". The amount of
energy transmitted between 10:00 and 11:00 on 2007-03-14 is recorded as
follows:&lt;/p&gt;

&lt;pre&gt;
[ sten:temporal_part_of :my_line ;
  a                     sten:classical_object ;
  a                     topology:directed_manifold_edge .
  sten:during           [ topology:end_1  [ sten:utc_iso8601 "2007-03-14T10:00" ] ;
                          topology:end_2  [ sten:utc_iso8601 "2007-03-14T11:00" ]
                        ]
]    sten:transmitted_energy  [ a            iso31:energy ;
                                joule_scale  [ basics:decimal  "360E6" ]
                              ] .
&lt;/pre&gt;
&lt;/div&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE 2 Consider the transmission line "my_line". The amount of
power transmitted at 10:30 on 2007-03-14 is recorded as
follows:&lt;/p&gt;

&lt;pre&gt;
[ sten:temporal_part_of :my_line ;
  a                     sten:classical_object_at_instant ;
  sten:at_time          [ sten:utc_iso8601 "2007-03-14T10:30" ]
]    sten:transmitted_power  [ a            iso31:power ;
                               watt_scale  [ basics:decimal  "0.1E6" ]
                             ] .
&lt;/pre&gt;
&lt;/div&gt;

&lt;p&gt;A property, such as &lt;b&gt;sten:transmitted_power&lt;/b&gt;, which is possessed by a
&lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt; cannot be possessed by a
&lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;. Instead a &lt;b&gt;sten:transmitted_power&lt;/b&gt;
can be associated with a &lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt; in two ways, as follows:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;by a derived property such as "mean transmitted power" or
"maximum transmitted power"; or&lt;/li&gt;
&lt;li&gt;by a transmitted power function over time.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The first of these approaches is a variant of the first, because
"mean" and "maximum" are properties of functions.&lt;/p&gt;

&lt;p&gt;A property of a &lt;a href="physical_things.htm#classical_object_at_instant"&gt;&lt;b&gt;sten:classical_object_at_instant&lt;/b&gt;&lt;/a&gt;,
such as &lt;b&gt;sten:transmitted_power&lt;/b&gt;, cannot be possessed by a
&lt;a href="physical_things.htm#classical_object"&gt;&lt;b&gt;sten:classical_object&lt;/b&gt;&lt;/a&gt;, even if it remains unchanged. In this case
the function over time is constant.&lt;/p&gt;

&lt;div class="note"&gt;
&lt;p&gt;EXAMPLE 3 Consider the transmitted power function over time for "my_line", which
is shown in
Figure &lt;a href="#transmitted_power_function_over_time_fig"&gt;5&lt;/a&gt;.&lt;/p&gt;

&lt;div align="center"&gt;
&lt;a name="transmitted_power_function_over_time_fig"/&gt;
&lt;img src="../images/transmitted_power_function_over_time.gif"
     alt="Transmitted power function over time"/&gt;
&lt;p class="caption"&gt;&lt;b&gt;Figure 5: Transmitted power function over time&lt;/b&gt;&lt;/p&gt;
&lt;/div&gt;

&lt;p&gt;The information can be recorded in OWL as follows:&lt;/p&gt;

&lt;pre&gt;
:my_line_from_2007-03-14T10:00_to_11:00
  sten:temporal_part_of :my_line ;
  a                     sten:classical_object ;
  a                     topology:directed_manifold_edge ;
  sten:during           [ topology:end_1  [ sten:utc_iso8601 "2007-03-14T10:00" ] ;
                          topology:end_2  [ sten:utc_iso8601 "2007-03-14T11:00" ] .

:my_line_from_2007-03-14T11:00_to_12:00
  sten:temporal_part_of :my_line ;
  a                     sten:classical_object ;
  a                     topology:directed_manifold_edge ;
  sten:during           [ topology:end_1  [ sten:utc_iso8601 "2007-03-14T11:00" ] ;
                          topology:end_2  [ sten:utc_iso8601 "2007-03-14T12:00" ] .

:my_line_from_2007-03-14T10:00_to_12:00
  sten:temporal_part_of :my_line ;
  a                     sten:classical_object ;
  a                     topology:directed_manifold_edge ;
  sten:during           [ topology:end_1  [ sten:utc_iso8601 "2007-03-14T10:00" ] ;
                          topology:end_2  [ sten:utc_iso8601 "2007-03-14T12:00" ] .

[ a                  basics:constant_function ;
  rdfs:domain        :my_line_from_2007-03-14T10:00_to_11:00 ;
  rdfs:range         iso31:power ;
  rdfs:subPropertyOf sten:transmitted_power ;
  basics:value_of_constant_function
                     [ a           iso31:power ;
		               watt_scale  [ basics:decimal  "0.1E6" ] ] .

[ a                  basics:constant_function ;
  rdfs:domain        :my_line_from_2007-03-14T11:00_to_12:00 ;
  rdfs:range         iso31:power ;
  rdfs:subPropertyOf sten:transmitted_power ;
  basics:value_of_constant_function
                     [ a           iso31:power ;
                       watt_scale  [ basics:decimal  "0.15E6" ] ] .

[ a                  basics:function ;
  rdfs:domain        :my_line_from_2007-03-14T10:00_to_12:00 ;
  rdfs:range         iso31:power ;
  rdfs:subPropertyOf sten:transmitted_power ;
  sten:function_mean [ a           iso31:power ;
                       watt_scale  [ basics:decimal  "0.125E6" ] ] .
&lt;/pre&gt;
&lt;/div&gt;

&lt;a name="function_property_ontology"/&gt;
&lt;h3&gt;4.7 Function property ontology&lt;/h3&gt;

&lt;a name="function_mean"/&gt;
&lt;h3&gt;4.7.1 function_mean&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#function_mean"&gt;&lt;b&gt;sten:function_mean&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;p&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; with domain &lt;b&gt;basics:function&lt;/b&gt;;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;for a function f:X &rarr; Y, it evaluates to give the member of Y as
follows:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;p&gt;as an integral:&lt;/p&gt;
&lt;table align="center"&gt;
&lt;tr&gt;
 &lt;td&gt;
  &lt;font size="+3"&gt;&int;&lt;/font&gt;&lt;sub&gt;&xlt;/sub&gt;
 &lt;/td&gt;
 &lt;td nowrap="nowrap" align="center"&gt;
  f(x) dx
 &lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
 &lt;td colspan="2"&gt;&lt;hr/&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
 &lt;td&gt;
  &lt;font size="+3"&gt;&int;&lt;/font&gt;&lt;sub&gt;&xlt;/sub&gt;
 &lt;/td&gt;
 &lt;td nowrap="nowrap" align="center"&gt;
  dx
 &lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;/li&gt;

&lt;li&gt;&lt;p&gt;as a sum:&lt;/p&gt;
&lt;table align="center"&gt;
&lt;tr&gt;
 &lt;td&gt;
  &lt;font size="+3"&gt;&sum;&lt;/font&gt;&lt;sub&gt;x &isin;&xlt;/sub&gt;
 &lt;/td&gt;
 &lt;td nowrap="nowrap" align="center"&gt;
  f(x)
 &lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
 &lt;td colspan="2"&gt;&lt;hr/&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
 &lt;td&gt;
  &lt;font size="+3"&gt;&sum;&lt;/font&gt;&lt;sub&gt;x &isin;&xlt;/sub&gt;
 &lt;/td&gt;
 &lt;td nowrap="nowrap" align="center"&gt;
  1
 &lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:ObjectProperty rdf:about="&sten;function_mean">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&basics;function"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#function_mean"/>
</owl:ObjectProperty>
<!--
&lt;/pre&gt;

&lt;a name="function_maximum"/&gt;
&lt;h3&gt;4.7.2 function_maximum&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#function_maximum"&gt;&lt;b&gt;sten:function_maximum&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; with domain &lt;b&gt;basics:function&lt;/b&gt;;&lt;/li&gt;
&lt;li&gt;for a function f:X &rarr; Y, it evaluates to give the member of Y that is the
maximum of f(x) for x &isin; X.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:ObjectProperty rdf:about="&sten;function_maximum">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&basics;function"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#function_maximum"/>
</owl:ObjectProperty>
<!--
&lt;/pre&gt;

&lt;a name="function_minimum"/&gt;
&lt;h3&gt;4.7.3 function_minimum&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#function_minimum"&gt;&lt;b&gt;sten:function_minimum&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; with domain &lt;b&gt;basics:function&lt;/b&gt;;&lt;/li&gt;
&lt;li&gt;for a function f:X &rarr; Y, it evaluates to give the member of Y that is the
minimum of f(x) for x &isin; X.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:ObjectProperty rdf:about="&sten;function_minimum">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&basics;function"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#function_minimum"/>
</owl:ObjectProperty>
<!--
&lt;/pre&gt;

&lt;a name="space_ontology"/&gt;
&lt;h3&gt;4.8 Space ontology&lt;/h3&gt;

&lt;a name="scope_of_the_space_ontology"/&gt;
&lt;h3&gt;4.8.1 Scope of the space ontology&lt;/h3&gt;

&lt;p&gt;Statements about how objects are placed in time and overlap in time
are crucial to the S-TEN project. S-TEN is only interested
in space in order to say where things are. The ontology in this section has been
derived directly from the ontology for time in order to serve the purpose of the
S-TEN project.&lt;/p&gt;

&lt;a name="physical_space"/&gt;
&lt;h3&gt;4.8.2 physical_space&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#physical_space"&gt;&lt;b&gt;sten:physical_space&lt;/b&gt;&lt;/a&gt; if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a partition of a part of the universe;&lt;/li&gt;
&lt;li&gt;there is an observer for which each item within the partition
consists of things which are at the same place.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;physical_space">
 <rdfs:subClassOf rdf:resource="&sten;classical_object"/>
 <rdfs:subClassOf rdf:resource="&topology;manifold"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#physical_space"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="point_in_space"/&gt;
&lt;h3&gt;4.8.3 point_in_space&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#point_in_space"&gt;&lt;b&gt;sten:point_in_space&lt;/b&gt;&lt;/a&gt;
if and only
if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:structure_point&lt;/b&gt;
within a &lt;a href="#physical_space"&gt;&lt;b&gt;sten:physical_space&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;point_in_space">
 <owl:equivalentClass>
  <owl:Restriction>
   <owl:onProperty rdf:resource="&basics;point_has_containing_structure"/>
   <owl:allValuesFrom rdf:resource="&sten;physical_space"/>
  </owl:Restriction>
 </owl:equivalentClass>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#point_in_space"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="part_of_space"/&gt;
&lt;h3&gt;4.8.4 part_of_space&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#part_of_space"&gt;&lt;b&gt;sten:part_of_space&lt;/b&gt;&lt;/a&gt; if and only
if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it has a &lt;a href="physical_things.htm#part_of"&gt;&lt;b&gt;sten:part_of&lt;/b&gt;&lt;/a&gt;
relationship with a &lt;a href="#physical_space"&gt;&lt;b&gt;sten:physical_space&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;part_of_space">
 <owl:equivalentClass>
  <owl:Restriction>
   <owl:onProperty rdf:resource="&sten;part_of"/>
   <owl:allValuesFrom rdf:resource="&sten;physical_space"/>
  </owl:Restriction>
 </owl:equivalentClass>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#part_of_space"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="region"/&gt;
&lt;h3&gt;4.8.4 region&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#region"&gt;&lt;b&gt;sten:region&lt;/b&gt;&lt;/a&gt; if and only
if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;a href="physical_things.htm#part_of_space"&gt;&lt;b&gt;sten:part_of_space&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it is a &lt;b&gt;topology:manifold&lt;/b&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;region">
 <owl:equivalentClass>
  <owl:Class>
   <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class rdf:resource="&sten;part_of_space"/>
    <owl:Class rdf:resource="&topology;manifold"/>
   </owl:intersectionOf>
  </owl:Class>
 </owl:equivalentClass>
 <owl:sameAs rdf:resource="&iso15926-2;spatial_location"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#region"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="wgs84_space"/&gt;
&lt;h3&gt;4.8.5 wgs84_space&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#wgs84_space"&gt;&lt;b&gt;sten:wgs84_space&lt;/b&gt;&lt;/a&gt; if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;a href="#physical_space"&gt;&lt;b&gt;sten:physical_space&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it is the domain of the scale
&lt;a href="http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html"&gt;Department of Defense, National Geophysical Agency (NGA) World Geodetic System 1984 (WGS 84)&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:Class rdf:about="&sten;wgs84_space">
 <rdf:type rdf:resource="&sten;physical_space"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#wgs84_space"/>
</owl:Class>
<!--
&lt;/pre&gt;

&lt;a name="occupies"/&gt;
&lt;h3&gt;4.8.6 occupies&lt;/h3&gt;
&lt;p&gt;An object is a &lt;a href="#occupies"&gt;&lt;b&gt;sten:occupies&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; from &lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt;
to &lt;a href="#part_of_space"&gt;&lt;b&gt;sten:part_of_space&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it specifies that the &lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt;
exists throughout the &lt;a href="#part_of_space"&gt;&lt;b&gt;sten:part_of_space&lt;/b&gt;&lt;/a&gt; and does not
exists outside the &lt;a href="#part_of_space"&gt;&lt;b&gt;sten:part_of_space&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:FunctionalProperty rdf:about="&sten;occupies">
 <rdf:type rdf:resource="&basics;function"/>
 <rdfs:domain rdf:resource="&sten;physical_thing"/>
 <rdfs:range rdf:resource="&sten;part_of_space"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#occupies"/>
</owl:FunctionalProperty>
<!--
&lt;/pre&gt;

&lt;a name="at"/&gt;
&lt;h3&gt;4.8.7 at&lt;/h3&gt;
&lt;p&gt;An object is an &lt;a href="#at"&gt;&lt;b&gt;sten:at&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:partial_function&lt;/b&gt; from
&lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt;
to &lt;a href="#point_in_space"&gt;&lt;b&gt;sten:point_in_space&lt;/b&gt;&lt;/a&gt;;&lt;/li&gt;
&lt;li&gt;it specifies that the
&lt;a href="physical_things.htm#physical_thing"&gt;&lt;b&gt;sten:physical_thing&lt;/b&gt;&lt;/a&gt; exists
at the &lt;a href="#point_in_space"&gt;&lt;b&gt;sten:point_in_space&lt;/b&gt;&lt;/a&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:ObjectProperty rdf:about="&sten;at">
 <rdfs:domain rdf:resource="&sten;physical_thing"/>
 <rdfs:range rdf:resource="&sten;point_in_space"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#at"/>
</owl:ObjectProperty>
<!--
&lt;/pre&gt;

&lt;a name="wgs84"/&gt;
&lt;h3&gt;4.8.8 wgs84&lt;/h3&gt;
&lt;p&gt;An object is an &lt;a href="#wgs84"&gt;&lt;b&gt;nga:wgs84&lt;/b&gt;&lt;/a&gt; relationship if and only if:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;it is a &lt;b&gt;basics:function&lt;/b&gt; from
&lt;a href="#wgs84_space"&gt;&lt;b&gt;sten:wgs84_space&lt;/b&gt;&lt;/a&gt; to
&lt;b&gt;basics:list_of_reals&lt;/b&gt;;&lt;/li&gt;
&lt;li&gt;it identifies points in space according to WGS84.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;u&gt;OWL specification:&lt;/u&gt;&lt;/p&gt;
&lt;pre&gt;
-->
<owl:FunctionalProperty rdf:about="&nga;wgs84">
 <rdfs:domain rdf:resource="&sten;wgs84_space"/>
 <meta:defined_by rdf:resource="&D2.1;/temporal_part_and_time.htm#wgs84"/>
</owl:FunctionalProperty>
<!--
&lt;/pre&gt;

&lt;/body&gt;
&lt;/html&gt;
-->

</rdf:RDF>
