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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Summarization of an inverse n-ary relation</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>28660 Boadilla del Monte</institution>
          ,
          <country country="ES">Spain</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Departamento de Inteligencia Artificial. Facultad de Informática. Universidad Politécnica de Madrid (UPM) Campus de Montegancedo</institution>
          ,
          <addr-line>s/n</addr-line>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Departamento de Inteligencia Artificial. Facultad de Informática. Universidad Politécnica de Madrid (UPM) Campus de Montegancedo</institution>
          ,
          <addr-line>s/n</addr-line>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Mari Carmen Suárez-Figueroa Ontology Engineering Group</institution>
          ,
          <addr-line>OEG</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>In this paper, we describe a logical ontology design pattern that summarizes a relationship and its inverse between two distinguished members of an n-ary relationship.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Ontology design pattern</kwd>
        <kwd>N-ary relation</kwd>
        <kwd>inverse relation</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>2. PATTERN DESCRIPTION</title>
    </sec>
    <sec id="sec-2">
      <title>2.1 Motivation</title>
      <p>
        It is well known that an n-ary relationship should be used to
address any of the following situations [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]:
a) A binary relationship that really needs a further argument.
      </p>
      <p>For example, to represent the distance between two places.
b) Two binary relationships that always go together and
should be represented as one n-ary relation. For example,
to represent the value of an observation (e.g. temperature
in a patient) and its trend.
1 http://www.w3.org/TR/swbp-n-aryRelations/
2
c) A relationship that is really amongst several things. For
example, to represent the spatial location of a person in a
given point of time.</p>
      <p>On the one hand, the motivation of this pattern is to express the
inverse relationship of an n-ary relation in which there are two
distinguished participants. This means that the relationship
exists mainly between two entities and the rest of entities
involved in the relationship can be considered as additional
arguments. This situation can also mean that there is a single
individual standing out as the subject or the "owner" of the
relation.</p>
      <p>On the other hand, the motivation is to provide a shortcut for
queries that involve two distinguished participants in the n-ary
relationship.</p>
      <p>This pattern is inspired on the third consideration shown in the
description of n-ary relations3 from the W3C Semantic Web
Best Practices Group (SWBP Group). The difference in our case
is that there are two distinguished participants in the
relationship. Therefore, this pattern could be considered as an
extension of the third consideration shown by the SWBP Group
applied to the use case of additional attributes describing a
relation4.
2.2 Aim
The aim of this pattern is to allow asking for n-ary relationships
and their inverse relations between two distinguished
participants without a complex query. Such a complex query
would involve the class created to support the n-ary relation
between the origin and destination classes of the n-ary
relationship.</p>
    </sec>
    <sec id="sec-3">
      <title>2.3 Solution description</title>
      <p>As it can be observed in Figure 1 the class "NAryRelationClass"
is the class created to support the n-ary relationship5 and its
further relations or attributes. The relationship
"mainRelationship" and its inverse relation have been created to
4 http://www.w3.org/TR/swbp-n-aryRelations/#useCase1
5</p>
      <p>
        This structure is created like in [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]
http://www.w3.org/TR/swbp-n-aryRelations/#useCase1
and
short-circuit the relation between the distinguished participants
in the n-ary relationship.
      </p>
      <p>&lt;&lt;owl::inverseOf&gt;&gt;</p>
      <p>InvolvedClass1</p>
      <p>InvolvedClassN
relationship1</p>
      <p>relationshipN
NAryRelationClass
-attribute1
-attributeM
mainRelationship
inverseMainRelationship
nAryRelationhip</p>
    </sec>
    <sec id="sec-4">
      <title>3. Example</title>
    </sec>
    <sec id="sec-5">
      <title>3.1 Problem example</title>
      <p>We might want to represent that a service provider provides a
service at a place in a given period of time with a particular
price. The model should also represent that a service is offered
by a provider.</p>
      <p>In this scenario, we have also observed that the queries executed
by our applications often ask for the relationship between
providers and their services and rarely ask for the relationships
about the services and where they are provided.
of ersServiceInTime
of ersServiceAtLocation
ServiceProvider of ersServiceAtPlaceInTimeWithPrice NAryRelationOffersServiceAtPlaceInTimeWithPrice of ersService
-hasServicePrice
serviceProvidedBy</p>
      <p>Service
&lt;&lt;owl: inverseOf&gt;&gt;</p>
    </sec>
    <sec id="sec-6">
      <title>3.2 Consequences</title>
      <p>The main advantage of this pattern is that allows asking for
those services that are provided by a service provider and
viceversa without a complex query. This complex query would
involve the class created to support the n-ary relation between
service providers and services.</p>
    </sec>
    <sec id="sec-7">
      <title>4. Related Work</title>
      <p>The origin of this pattern is the Logical Pattern for Modelling
N-ary Relation: Introducing a New Class for the Relation
pattern6 and the third consideration shown in the description of
n-ary relations from the W3C SWBP Group. Therefore, this
pattern is related to and can be used in combination with the
Logical Pattern for Modelling N-ary Relation: Introducing a
New Class for the Relation.</p>
    </sec>
    <sec id="sec-8">
      <title>5. Summary and Outlook</title>
      <p>The Summarization of an inverse n-ary relation pattern allows
us to speed up the queries involving relationships between two
distinguished participants in an n-ary relation.</p>
      <p>Future lines of work will address the problem of summarizing
the relationships and their inverse between a set of distinguished
member (at least three) into an n-ary relationship.</p>
      <p>In addition, the elaboration of guidelines that explain in detail
how to identify the distinguished members in an n-ary
relationship would be very useful to extend the pattern
description and to facilitate its use.</p>
    </sec>
    <sec id="sec-9">
      <title>6. ACKNOWLEDGMENTS</title>
      <p>This work has been partially supported by the Spanish project
mIO! (CENIT-2008-1019).</p>
    </sec>
  </body>
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