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NOTE-rdf-uml-19980804
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<H1 class="maintitle" align="center" STYLE="text-align: center">
A Discussion of the Relationship Between RDF-Schema and UML
</H1>
<p align=center STYLE="text-align: center">
<strong>W3C Note 04-Aug-1998</strong>
</p>

<center><a href="/1998/.status/NOTE-rdf-uml-19980804/status"><img src="/1998/.status/NOTE-rdf-uml-19980804/statusimg" border=0 alt="Status of this Document"></a></center>

<div class="intro">

<dl>
<dt>This document:
<dd>
<A HREF="http://www.w3.org/TR/1998/NOTE-rdf-uml-19980804/">http://www.w3.org/TR/1998/NOTE-rdf-uml-19980804</A>

<dt>Author:
<dd><a href="mailto:wchang@adobe.com">Walter W. Chang</a>, Advanced Technology Group, Adobe Systems
</dl>

<H2>Status of This Document</H2>

<p>This document is a
<a href="http://www.w3.org/Consortium/Process/#Notes">NOTE</a> made
available by W3C for discussion only. This indicates no endorsement of
its content, nor that W3C has had any editorial control in its
preparation, nor that W3C has, is, or will be allocating any resources
to the issues addressed by the NOTE.</p>

<P>Comments may be sent to
<A HREF="mailto:www-rdf-comments@w3.org">www-rdf-comments@w3.org</A>.
All mail is
<A HREF="http://lists.w3.org/Archives/Public/www-rdf-comments/">archived</a>
and available for review.</p>
</div>
<hr>

<h2>Introduction</h2>

<P>This note summarizes the relationship between RDF-Schema and
UML, the generic industry standard object-oriented modeling framework
for information systems modeling. This note will briefly describe
these systems then relate them to each other.</P>

<H2>RDF-Schema</H2>

<P>RDF-Schema specifies information about classes in a schema,
including properties (attributes) and relationships between classes.
RDF-Schema provides a typing system: informally, it is a basic
set of nodes and relations that can be used to express properties
of classes of the schema. RDF-Schema includes a facility to indicate
that certain classes are subclasses of others, and provides a
small number of basic classes. Finally, it contains a facility
for specifying a small number of constraints such as the cardinality
(number of occurrences) required and permitted of properties of
instances of classes.</P>

<P>&quot;RDF-Schemas are specified using a declarative representation
language influenced by ideas from knowledge representation, e.g.,
semantic nets, frames, and predicate logic, as well as database
schema representation models such as binary relational models
([NIAM], etc.) and graph data models. The RDF schema specification
language is less expressive, but simpler, than full predicate
calculus languages such as CycL [CycL] and KIF [KIF].&quot;</P>

<H2>UML</H2>

<P>The Unified Modeling Language (UML) is a framework for describing
a set of models that capture the functional and structural semantics
of any complex information system. UML defines the following models
for representing such systems:</P>

<P>1. A use case model that states the requirements of the user<BR>
2. A class model that captures the static information structure
of objects<BR>
3. A state model that describes the dynamic behavior of objects
<BR>
4. An activity implementation model that describes work unit actions<BR>
5. An interaction model that models scenarios and message flows<BR>
6. A deployment model that describes how software subsystems are
allocated<BR>
to actual hardware components</P>

<H2>How RDF and UML Relate to Each Other</H2>

<P>Web-based and non-Web based applications can be described by
a number of schema specification mechanisms, including RDF-Schema.
The RDF-Schema model itself is equivalent to a subset of the class
model in UML. RDF-Schema uses a DLG (Directed Labeled Graph) model
for describing schemas.</P>

<P>Class schemas expressed in UML can be viewed also as DLGs.
If a DLG is used for a class model schema in UML, the RDF-Schema
DLG can be shown to be isomorphic to a subgraph of the UML class
schema DLG. This is possible because RDF-Schema elements map directly
into UML class model elements.</P>

<P>In addition, the DAG formed by considering RDF-Schema subClassOf
class inheritance structures maps directly to UML class generalization
DAGs, RDF class properties map to UML class attributes, and RDF
properties and property cardinality constraints map to UML associations
and association <BR>
constraints.</P>

<P>The various constructs and elements in the class models of
UML (#2.) and RDF-Schema readily map between each other. While
currently the RDF-Schema work does not have counterparts to the
other 5 remaining UML modeling areas, RDF-Schema could be extended
to support these models as well.</P>

<P>Given that an application schema can be described by RDF-Schema
(or UML), how do RDF-Schema and UML actually relate to each other?
The remainder of this note describes the relationship between
the elements of the class models for RDF-Schema and UML. An outline
is presented below to show how a given schema represented by the
RDF-Schema model can be transformed into an equivalent UML class
schema representation.</P>

<P>Further, given any UML class schema representation, we can
specify an equivalent RDF-Schema representation.</P>

<H2>Comparison of Models</H2>

<P>Outlined below are the steps for showing that class schema
representations using RDF-Schema and the class model subset of
UML are equivalent.</P>

<P><CENTER><TABLE WIDTH="515" BORDER="1" CELLSPACING="2"
CELLPADDING="0">
  <TR>
    <TD WIDTH="25%" HEIGHT="25">
    &nbsp;Step</TD>
    <TD WIDTH="75%">
    <P><CENTER>&nbsp;Description</CENTER></TD>
  </TR>
  <TR>
    <TD HEIGHT="47">
    &nbsp;1.</TD>
    <TD>
    Show that RDF-Schema and UML classes map between each other.&nbsp;</TD>
  </TR>
  <TR>
    <TD HEIGHT="47">
    &nbsp;1a.</TD>
    <TD>
    Show that single and multiple class inheritance constructs in
    each system maps to the other.&nbsp;</TD>
  </TR>
  <TR>
    <TD HEIGHT="68">
    &nbsp;1b.</TD>
    <TD>
    Show that the class inheritance DAGs for RDF-Schema and UML (using
    RDF-Schema subClassOf and UML subclass relationships respectively)
    are isomorphic.&nbsp;</TD>
  </TR>
  <TR>
    <TD HEIGHT="89">
    &nbsp;1c.</TD>
    <TD>
    Note that RDF-Schema does not explicitly support the notion of
    operations or methods, We ignore this for now. When RDF-Schema
    supports this, map these methods into UML operations.</TD>
  </TR>
  <TR>
    <TD HEIGHT="68">
    &nbsp;2.</TD>
    <TD>
    Show that RDF-Schema properties and UML attributes can be directly
    mapped between each other. Extensions can be added later to support
    this if necessary.&nbsp;</TD>
  </TR>
  <TR>
    <TD HEIGHT="47">
    &nbsp;3.</TD>
    <TD>
    Show that any UML associations can be expressed as RDF-Schema
    properties.&nbsp;</TD>
  </TR>
  <TR>
    <TD HEIGHT="46">
    &nbsp;3a.</TD>
    <TD>
    Show that UML multiplicity constraints on associations are equivalent
    to a subset of RDF-Schema cardinality constraints</TD>
  </TR>
  <TR>
    <TD HEIGHT="44">
    &nbsp;3b.</TD>
    <TD>
    Show that property naming and reification in RDF-Schema maps
    to UML association names and attributes.&nbsp;</TD>
  </TR>
  <TR>
    <TD HEIGHT="84">
    &nbsp;4.</TD>
    <TD>
    Show that while currently missing from RDF-Schema, a generalized
    constraint model can be created by extending RDF-Schema using
    reification allowing it to map into the general UML Class constraint
    model.&nbsp;</TD>
  </TR>
  <TR>
    <TD HEIGHT="84">
    &nbsp;5.</TD>
    <TD>
    Having accomplished 1,2, and the portion of 3 relevant to the
    RDF-Schema, we can then show that the full RDF-Schema DLG can
    map into a proper subgraph of the UML class model DLG.&nbsp;</TD>
  </TR>
</TABLE></CENTER>

<P><BR>
As noted, because UML contains additional modeling constructs
not found in RDF-Schema, full specification using UML may result
in a DLG model that is a superset of the model specified by RDF-Schema.
However, as indicated earlier, extensions to the RDF-Schema model
could be made to support these class model constructs as well
as other UML system models as needed by future application schemas
that use RDF-Schema.</P>

<H2>How RDF-Schema Properties and UML Roles Relate</H2>

<P>We note that RDF-Schema properties can correspond to UML roles,
and when a PropertyType actually names a range that is another
RDF-Schema class, one way this can be viewed is that the RDF-Schema
property is in fact being used as an association in the UML sense.
More precisely, an RDF-Schema property corresponds to a named
role within an unnamed association. UML has some facilities here
(such as naming associations and associating roles) that RDF-Schema
does not. [Layman,1]</P>

<P>[Wickstead] has presented several good examples of this in
the context of RDF-Schema WG discussions about non-Web resource
identifiers: he suggests that instead of introducing database
Primary/Foreign Keys, we let properties name actual classes. This
would cause the property to be used as an association to other
objects constrained by whatever cardinality constraint was specified.</P>

<H2>Conclusion</H2>

<P>A class of application schemas can be described by RDF-Schema.
RDF-Schema in turn can be shown to map into a subset of the UML
framework through inheritance schema DAG isomorphism and isomorphism
of RDF-Schema DLGs to a subgraph of UML full schema DLGs using
the procedure outlined above.</P>

<P>Thanks to Ron Daniels for his careful review of earlier draft
versions of this document and his comments and suggestions.</P>

<H2>Appendix 1</H2>

<H3>Summary of Schema Model Differences Between RDF-Schema and UML</H3>

<P>The table below summarizes how the two different schema modeling
systems support specific object constructs.</P>

<P><CENTER><TABLE WIDTH="450" BORDER="1" CELLSPACING="2"
CELLPADDING="0">
  <TR>
    <TD WIDTH="36%" HEIGHT="24">
    Construct</TD>
    <TD WIDTH="29%">
    RDF-Schema</TD>
    <TD WIDTH="35%">
    UML</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    Classes</TD>
    <TD>
    Y</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Members</TD>
    <TD>
    Properties</TD>
    <TD>
    Attributes</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Methods</TD>
    <TD>
    N</TD>
    <TD>
    Operations</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Generalization</TD>
    <TD>
    Y, S.I., M.I.</TD>
    <TD>
    Y, S.I., M.I.</TD>
  </TR>
  <TR>
    <TD HEIGHT="44">
    - Visibility of Attr/Meth.</TD>
    <TD>
    Public</TD>
    <TD>
    Public (1), Protected (2), and Private (3)</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Interfaces</TD>
    <TD>
    N</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Template Classes</TD>
    <TD>
    N</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Utility Classes</TD>
    <TD>
    N</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    Associations</TD>
    <TD>
    Y</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Assoc. Naming</TD>
    <TD>
    via Properties</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Role Naming</TD>
    <TD>
    via Properties</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Cardinality</TD>
    <TD>
    &nbsp;</TD>
    <TD>
    (6)</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - - - One</TD>
    <TD>
    ExactlyOne</TD>
    <TD>
    1</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - - - Zero or One</TD>
    <TD>
    ZeroOrMore</TD>
    <TD>
    0..1</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - - - From 0 to N</TD>
    <TD>
    ZeroOrMore</TD>
    <TD>
    0..N</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - - - From 1 to N</TD>
    <TD>
    OneOrMore</TD>
    <TD>
    1..N</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - - - From M to N</TD>
    <TD>
    No</TD>
    <TD>
    M..N</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - General Constraints</TD>
    <TD>
    N</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Association Classes</TD>
    <TD>
    N</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - N-ary Associations</TD>
    <TD>
    reification</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    - Association Qualifiers</TD>
    <TD>
    N</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    Aggregation</TD>
    <TD>
    Y (4)</TD>
    <TD>
    Y</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    Navigation</TD>
    <TD>
    Y</TD>
    <TD>
    Y (5)</TD>
  </TR>
  <TR>
    <TD HEIGHT="24">
    MetaModel</TD>
    <TD>
    Y</TD>
    <TD>
    Y (7)</TD>
  </TR>
</TABLE></CENTER>

<H3>Table Notes:</H3>

<P>(1) Public - the element is visible to all clients of the class.<BR>
(2) Protected - the element is visible only to the subclass of
the class.<BR>
(3) Private - the element is visible to only the class itself.<BR>
(4) UML distinguishes between aggregation and composition: aggregation
is an abstract modeling, composition is a containment model
that can correspond to the RDF-Schema collection, bag, or
sequence constructs.<BR>
(5) RDF-Schema can use directed arcs, UML uses directed associations.<BR>
(6) RDF-Schema cardinality constraints are a subset of UML multiplicity
constraints. UML allows specification of multiplicity information
at
both ends of an association. RDF-Schema currently does not directly
support cardinality constraints besides the 4 listed. Supporting
arbitrary cardinalities e.g., 2-100 times would be useful, as
well as
intervals e.g., 3..5,17..23 would be useful. In the table, M and N
are integers &gt; 1.<BR>
(7) While both RDF-Schema and UML have MetaModels, it is worth
pointing
out that the UML meta model is both substantially more elaborate
and
different than that of RDF-Schema meta model. [Layman,2]<BR>
(8) We note that the intended usages for RDF-Schema and UML may
differ.
While both systems can describe schemas, each system may be better
suited for a particular application. Eg., databases are described
by
schemas defining tables, views, referential integrity constraints,
and other database mechanisms; models of tree-structure grammars
such
as XML are described by schemas such as XML DTDs; models of entities
and relations are described in E-R schemas such as UML; models
of
nodes and arcs are described by node-and-arc schemas such as RDF
schemas. While there is substantial overlap between RDF and UML,
we anticipate that each will be used to describe somewhat different
entities. [Layman,2]</P>

<H2>References:</H2>

<P>[Rumbaugh et. al.] Jim Rumbaugh, Ivar Jacobson, and Grady Booch,
Unified
Modeling Language Reference Manual, ISBN: 0-201-30998-X, Addison
Wesley,
est. publication December 1997.</P>

<P>[RDF M+S] <A HREF="http://www.w3.org/TR/WD-rdf-syntax">Resource Description Framework, (RDF) Model and Syntax</A>,
W3C
Working Draft 16 Feb 1998, http://www.w3.org/TR/WD-rdf-syntax
,<BR>
Ora Lassila &lt;<A HREF="mailto:ora.lassila@research.nokia.com">ora.lassila@research.nokia.com</A>&gt;, Nokia Research
Center<BR>
Ralph R. Swick &lt;<A HREF="mailto:swick@w3.org">swick@w3.org</A>&gt;, World Wide Web Consortium
<BR>
et. al.</P>

<P>[RDF-Schema] <A HREF="http://www.w3.org/RDF/Group/WD-rdf-schema">Resource Description Framework, (RDF) Schemas</A>,
W3C Working
Draft 1 May 1998, http://www.w3.org/RDF/Group/WD-rdf-schema ,<BR>
Dan Brickley, University of Bristol, R.V. Guha, Netscape, Andrew
Layman, <BR>
Microsoft.</P>

<P>[UML-Tk] Hans-Erik Eriksson and Magnus Penker, &quot;UML Toolkit&quot;,
John Wiley &amp; <BR>
Sons, New York, 1997.</P>

<P>[IUML] Pierre-Alain Muller. &quot;Instant UML&quot;, Wrox Press
Ltd., Birmingham, <BR>
UK, 1997. Original French Edition: &quot;Modelisation objet avec
UML&quot;, <BR>
Editions Eyrolles, Paris France, 1997.</P>

<P>[NIAM] G. M. Nijssen and Terry Halpin, Conceptual Schema and
Relational <BR>
Database Design, (Prentice Hall, Sydney:1989)</P>

<P>[CycL] CycL: The CYC Representation Language; <BR>
<A HREF="http://www.cyc.com/tech.html#cycl">http://www.cyc.com/tech.html#cycl</A></P>

<P>[KIF] Knowledge Interchange Format (KIF); <BR>
<A HREF="http://logic.stanford.edu/kif/kif">http://logic.stanford.edu/kif/kif</A>.</P>

<P>[Wicksteed] Charles Wicksteed, Reuters.<BR>
<A HREF="/1998/08/NOTE-rdf-uml-19980804-references">Working Group mail archive</a>
(<a href="/Consortium/Prospectus/Joining">member only</a>)</p>

<P>[Layman], Andrew Layman. Microsoft Corporation.<BR>
<A HREF="/1998/08/NOTE-rdf-uml-19980804-references">Working Group mail archive</a>
(<a href="/Consortium/Prospectus/Joining">member only</a>)</p>

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