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      RDF Diff, Patch, Update, and Sync -- Design Issues
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    <div class="online">
      <a href="./">Up to Design Issues</a>
    </div>
    <div class="maketitle">
      <h1 class="title">
        Delta: an ontology for the distribution of differences
        between RDF graphs
      </h1>
      <address>
        <a rel="author" href=
        "http://www.w3.org/People/Berners-Lee/">Tim Berners-Lee</a>
        and <a rel="author" href=
        "http://www.w3.org/People/Connolly/">Dan Connolly</a>,
        <a rel="institute" href="http://www.csail.mit.edu/">MIT
        Computer Science and Artificial Intelligence Laboratory
        (CSAIL)</a><br />
        <span class="thanks">This work is supported in part by
        funding from US Defense Advanced Research Projects Agency
        (DARPA) and Air Force Research Laboratory, Air Force
        Materiel Command, USAF, under agreement number
        F30602-00-2-0593, <q>Semantic Web
        Development</q>.</span><br />
        <span class="online">Created: 2001, current: $Revision:
        1.114 $ of <!--linebreak-->
         $Date: 2009/08/27 21:38:06 $</span><br />
        <span class="online">Status: personal view only. Editing
        status: rough. 2004/03: Extended to add pointers to
        implementations, and details of actual language used. see
        also: <a href=
        "http://lists.w3.org/Archives/Team/sw-team/2004Jul/0008">comments
        from reviewers</a></span>
      </address>
      <p class="online">
        Keywords: RDF, Difference, patch, remote update,
        synchronization, graph comparison.
      </p>
    </div>
    <hr />
    <div class="abstract">
      <h4>
        Abstract
      </h4>
      <p>
        The problem of updating and synchronizing data in the
        Semantic Web motivates an analog to text diffs for RDF
        graphs. This paper discusses the problem of comparing two
        RDF graphs, generating a set of differences, and updating a
        graph from a set of differences. It discusses two forms of
        difference information, the context-sensitive <q>weak</q>
        patch, and the context-free <q>strong</q> patch. It gives a
        proposed <strong>update ontology</strong> for patch files
        for RDF, and discusses experience with proof of concept
        code.
      </p>
    </div>
    <h2>
      Introduction
    </h2>
    <p>
      The use of text files to record programs, documents, and
      other artifacts is supported by version control systems such
      as RCS<a href="#Tich85">[Tich85]</a> and CVS<a href=
      "#Ber90">[Ber90]</a> that are based on the ability to compute
      the difference between two text files and represent it as
      diff<a href="#Mill85">[Mill85]</a>, i.e. a set of editing
      instructions. The use of database tables to record bank
      accounts and records of all sorts is supported by the
      relational calculus<a href="#Codd70">[Codd70]</a> and its
      expression as SQL statements. In both cases, the data goes
      thru a sequence of states; not only are the states
      represented explicitly (as text files or database tables) but
      also the transitions from one state to the other can be
      represented explicitly (either as editing instructions or SQL
      insert/update statements). Difference (<samp>\Delta</samp>)
      and sum (<samp>\Sigma</samp>) functions are ubiquitous in
      computing and, like differentiation and integration, are
      inverse in the sense that:
    </p>
    <p class="eqn-display">
      v1 = <samp>\Sigma</samp>(v0, <samp>\Delta</samp>(v0, v1))
    </p>
    <p>
      Since the transitions can be represented much more compactly
      than the pairs of states, and the sigma function is
      straightforward to compute, the deltas are useful for
      efficiently updating data distributed among two or more
      peers.
    </p>
    <p>
      We are developing a Semantic Web Application Platform
      (<a href="/2000/10/swap/">SWAP</a>) including tools and
      applications to manipulate RDF graphs much like traditional
      tools manipulate text files. It includes <code>cwm</code>, a
      command-line tool for processing RDF in both the standard XML
      encoding<a href="#RDF04">[RDF04]</a> and an experimental
      encoding, Notation3 (n3)<a href="#Ber03">[Ber03]</a>.
    </p>
    <p>
      As we build the Semantic Web, using RDF graphs<a href=
      "#RDFC04">[RDFC04]</a> to represent data such as
      bibliographies<a href="#DC02">[DC02]</a>, syndication
      summaries<a href="#RSS">[RSS]</a> and medical
      terminology<a href="#Gol03">[Gol03]</a>, we see a need for
      difference and sum functions for RDF graphs. The use of RDF
      to represent test results<a href="#EARL">[EARL]</a>,<a href=
      "#OWLT">[OWLT]</a> motivates better ways to compare the
      actual results of software tests with the intended results
      and isolate the differences.
    </p>
    <h3>
      <a name="Synchroniz" id="Synchroniz">The Synchronization
      Problem</a>
    </h3>
    <p>
      One of the most stubborn problems in practical computing is
      that of synchronizing calendars and address books between
      different devices. Various combinations of device and
      program, from the same or different manufacturers, produce
      very strange results on not-so-rare occasions.
    </p>
    <p>
      The problem has three parts. There is the syntactic problem
      of extracting the data from the strange device or its storage
      medium and turning into something manageable, such as RDF.
      There is the semantic problem of understanding what the
      fields mean: can one have two home phone numbers? There is
      the problem of actually synchronizing changes, particularly
      in the general case that changes have been made on both
      devices.
    </p>
    <p>
      Because the direct syntactic conversion to RDF often leaves
      something which has strained and awkward semantics, it is
      often necessary or tempting to mix the semantic and syntactic
      conversions. <span class="online">(See <a href=
      "/2002/12/cal/" class="online">RDF calendaring</a>
      discussions.)</span> Because the merging of changes requires
      more application knowledge than the bare RDF data provides,
      it is tempting to mix the conversion and sync algorithm.
      However, this mixing reduces the modularity and testability
      of the resulting program. Perhaps if the three stages were
      separated, then a more robust system, and one more extensible
      by the addition of information in new ontologies, would
      result.
    </p>
    <p>
      In the semantic web architecture, the application constraints
      on the data can be represented in the ontology, and so can be
      used by a a generic synchronization system.
    </p>
    <p>
      On the one hand, the syntactic problems are straightforward,
      if tedious, and the much harder semantic problems may explain
      why many existing synchronization packages break down. But on
      the other hand, perhaps it is the combination of the two that
      result in so many failures; perhaps software that separates
      the problems, treating synchronization generically, will be
      more robust. We hope this work contributes to further work on
      specifications such as SyncML<a href="#Sync02">[Sync02]</a>.
    </p>
    <p>
      And while in the general case, concurrent changes may be
      completely irreconcilable, the diff mechanisms discussed here
      solve an interesting part of the problem space.
    </p>
    <h3>
      Problems with the line-oriented approach
    </h3>
    <p>
      RDF graphs can be serialized and used with traditional
      line-oriented tools. In the general case, with no constraints
      on how the graphs are serialized, line-oriented deltas can be
      as large as the data itself, even between files representing
      the same graph. However, when files are edited by hand, small
      changes to the data naturally result in small textual diffs.
      But since the difference is expressed as the difference
      between two text files, not the difference between two
      graphs, the delta is dependent on the graph serialization.
      It's not enough to have the original graph to use the delta;
      one needs a copy of the particular serialization.
    </p>
    <p>
      Pretty-printing algorithms reduce the large number of
      possible serializations of an RDF graph to a few actual
      serializations. The difference engine<a href=
      "#Kly04">[Kly04]</a> produces human-readable difference
      descriptions using an algorithm analogous to comparing
      pretty-printed graphs; its descriptions are not sufficient to
      reconstruct one graph from the other, however.
    </p>
    <p>
      We find it practical to use CVS to manage both hand-edited
      and machine-serialized RDF data files in many cases. A
      notable exception is the reference results for tests:
      comparison of experimental test results versus reference
      results yield many false test failures every time we change
      the pretty-printing algorithm in the slightest. The cost of
      managing the reference results this way is barely tolerable.
    </p>
    <p>
      The straightforward pretty-printing algorithm works in the
      obvious way when all the nodes are named (either with URIs or
      literals): triples are sorted by subject, and those that
      share a subject are grouped together. Notation3 has syntax
      for grouping triples that shared predicates. Unlabeled nodes
      (<em>blank nodes</em> or <em>bnodes</em>) that have no
      incoming triples are treated like named subjects. Bnodes that
      have one incoming link serve as internal nodes in the
      pretty-printing tree. Bnodes that have more than one incoming
      triple are given arbitrary labels for the purpose of
      serialization and are hence treated like named subjects. For
      example, the triples
    </p>
    <pre class="example">
:Bob :pet _:p.
_:p :size "small".
:Bob :brother :Pete.
_:p :mother _:p2.
:Pete :pet _:p2.
</pre>
    <p>
      are pretty-printed as
    </p>
    <pre class="example">
    :Bob     :brother :Pete;
         :pet  [
             :mother _:g0;
             :size "small" ] .

    :Pete     :pet _:g0 .
</pre>
    <p>
      The ordering and the identification of bnodes are the two
      ways which serializations of the same graph can arbitrarily
      differ. <code>Cwm</code> not only attempts to find a
      serialization which minimizes the number of arbitrarily named
      nodes but often happens to regenerate arbitrary names
      consistently across runs. Even so, diffs of pretty-printed
      RDF are still unsatisfactory, since changes as small as one
      triple can lead to arbitrarily large textual diffs if that
      triple changes the set of bnodes that need arbitrary labels.
    </p>
    <p>
      To completely eliminate the arbitrary choices in how to
      serialize an RDF graph, we could employ a canonicalization
      algorithm such as the one<a href="#Car03s">[Car03s]</a> in
      Jena<a href="#Car03">[Car03]</a>, or <a href=
      "/2000/10/swap/cant.py">cant.py</a> from our own SWAP
      toolkit. One problem with this approach is that the canonical
      form is expressed in the N-Triples<a href=
      "#RDFT04">[RDFT04]</a> representation. Deltas between
      N-Triples files are verbose and tedious to read for most
      practical graphs. Further, the problem of large textual diffs
      resulting from small changes remains: these canonicalization
      algorithms work by computing a signature for each blank node
      based on nearby triples and sorting the results; adding or
      removing one triple near a blank node will change its
      signature and hence potentially the labeling of many bnodes.
    </p>
    <h2>
      Goals: Economy and Robustness
    </h2>
    <p>
      SQL statements and text file diffs are attractive because
      they succinctly represent the difference between two states.
      If the difference between two text files were not much
      smaller than either of the text files, it would be of little
      use. The essential feature of a difference algorithm, then,
      is <em>economy</em>: small differences between input states
      should result in small deltas.
    </p>
    <p>
      Much of the popularity of CVS is due to its support of
      concurrent development. It makes a patch file<a href=
      "#Wall">[Wall]</a> representing the changes each party has
      made. These changes are made, in order, to the repository
      file to generate new versions. In the event that two agents
      take a copy of the same version <samp>v0</samp> and make
      different changes to it (<samp>v1a</samp> and
      <samp>v1b</samp>), the party that commits last attempts to
      make <samp>v1</samp> which incorporates both diffs:
    </p>
    <p class="eqn-display">
      v1 = <samp>\Sigma</samp>(<samp>\Sigma</samp>(v0,
      <samp>\Delta</samp>(v0, v1a)), <samp>\Delta</samp>(v0, v1b))
    </p>
    <p>
      Note that <samp>\Delta(v0, v1b)</samp> is applied to
      something other than v0. The context diff and unidiff formats
      are sufficiently robust that it does work in most practical
      cases. When it does not work, then the user is left with the
      problem of manually reconciling the conflicts. This happens
      when, for example, one party moves the date of a meeting at
      the same time as someone else moves or deletes the meeting.
      It may be that the criterion that a problem needs human
      involvement is very application-dependent.
    </p>
    <p>
      There are thee failure modes:
    </p>
    <ol>
      <li>Inconsistent changes were made. This failure mode is not
      automatically soluble.
      </li>
      <li>The patch was incapable of finding the appropriate points
      in v1a at which to make the change <samp>\Delta</samp>(v0,
      v1b). This form of failure we can eliminate for certain RDF
      graph deltas.
      </li>
      <li>The patch was misapplied: the context was used to
      determine points at which to make the change, but the wrong
      point was used, and erroneous data resulted. This is
      unacceptable.
      </li>
    </ol>
    <p>
      A <em>robust</em> patch is one which may be applied so a file
      different to the one it was originally generated from,
      without being misapplied and hence generating erroneous
      information. In the line oriented tools, the <em>patch</em>
      program was introduced to be more robust than simply applying
      the patch as a series of editor commands.
    </p>
    <h2>
      Delta and Sigma for RDF Graphs
    </h2>
    <p>
      An RDF graph is a set of (subject, predicate, object)
      triples, i.e. a set of typed links between nodes. Each node
      may or may not be named (either by a URI or a literal). As a
      measure of the size of the difference between two RDF graphs
      <samp>G1</samp> and <samp>G2</samp>, one can use the sum of
      the size of the set differences <samp>|G1-G3|</samp> and
      <samp>|G2-G3|</samp> where <samp>G3</samp> is the largest
      common subgraph of <samp>G1</samp> and of <samp>G2</samp>.
    </p>
    <h3>
      Computing differences between RDF graphs
    </h3>
    <p>
      In the case in which all the nodes are named, computing the
      difference between two graphs is simple and straightforward:
    </p>
    <p class="definition">
      If <samp>G1</samp> and <samp>G2</samp> are ground RDF graphs,
      then the <em>ground graph delta</em> of <samp>G1</samp> and
      <samp>G2</samp> is a pair <samp>(insertions,
      deletions)</samp> where <samp>insertions</samp> is the set
      difference <samp>G2-G1</samp> and <samp>deletions</samp> is
      <samp>G1-G2</samp>.
    </p>
    <p>
      This form of delta is reasonably economical: the storage cost
      is linear in the size of the difference between the graphs.
      Straightforward extensions with slightly improved economy
      might be more specific in expressing differences in which
      only one or two parts of the triple have changed.
    </p>
    <p>
      It is also completely robust. Each statement is independent,
      with no variables: there is no cause for ambiguity. The
      deletion statements may be deleted from, and the insertion
      statements added to, any graph.
    </p>
    <p>
      In the case where not all of the nodes are named, finding the
      largest common subgraph becomes a case of the graph
      isomorphism problem. The arc labels do have names (in a very
      large set of practical cases, including all those which can
      be serialized as RDF/XML). Graph isomorphism is in fact a
      class of difficult problem that cannot be solved in
      polynomial time but which has not been shown to be NP
      complete<a href="#Kob93">[Kob93]</a>. While the general graph
      isomorphism problem has readily available solutions<a href=
      "#Ski97">[Ski97]</a><a href="#Ski01">[Ski01]</a>, they do not
      seem to be a good match for the practical cases of RDF graph
      diff.
    </p>
    <p>
      There is an interesting subset of real cases in which there
      are a mixture of named and unnamed nodes, but none of the
      unnamed nodes is very far from a named node. In this case,
      the unnamed nodes can be indirectly identified by giving a
      path from a named node. The difference is then expressed by
      giving this local context and the related changes.
    </p>
    <h3>
      A patch file format for RDF deltas
    </h3>
    <p>
      By analogy to the text diff, there is a need not only for a
      difference-finding algorithm, but for a patch file format.
      Such a format needs:
    </p>
    <ul>
      <li>a way to uniquely identify what is changing
      </li>
      <li>a way to distinguish between the pieces added and those
      subtracted
      </li>
    </ul>
    <p>
      It is straightforward to pinpoint the parts of the graph that
      have changed when all nodes are named, but less so in the
      presence of anonymous nodes.
    </p>
    <p>
      To identify what is changing, we use Notation3 expressions
      for quoted RDF graphs with schema variables, and we introduce
      three new terms. For example:
    </p>
    <pre class="example">
@prefix diff: &lt;http://www.w3.org/2004/delta#&gt;.
{ ?x  bank:accountNo "1234578"; bank:balance 4000}
 diff:replacement
{ ?x  bank:accountNo "1234578"; bank:balance 3575}.
</pre>
    <p>
      This one new property <code>replacement</code> can express
      any change. Deletions can be written <code>{...}
      diff:replacement {}</code> and additions can be written
      <code>{} diff:replacement {...}</code>.
    </p>
    <p>
      The second alternative is very similar but involves two
      properties, one for inserting and one for deleting:
    </p>
    <pre class="example">
{ ?x  bank:accountNo "1234578"}
  diff:deletion  { ?x  bank:balance 4000};
  diff:insertion { ?x  bank:balance 3575}.
</pre>
    <p>
      The form using <code>diff:insertion</code> and
      <code>diff:deletion</code> is implemented in <a href=
      "/2000/10/swap/doc/cwm">cwm</a>.
    </p>
    <p>
      The first and second form are related by
    </p>
    <pre class="definition">
{ ?F replacement ?G }    &lt;=&gt;  { ?F deletion ?F; insertion ?G }
</pre>
    <h3>
      Weak and Strong diffs
    </h3>
    <p>
      To address robustness, we distinguish two types of RDF graph
      deltas: a <em>weak</em> delta gives enough information to
      apply it to exactly the graph it was computed from, but a
      <em>strong</em> delta specifies the changes in a
      context-independent manner. The difference is not in the
      patch file format, but in the information a particular patch
      gives.
    </p>
    <p>
      Returning to the bank example, if bank account numbers are
      globally unique, then the replacement pattern will bind ?x to
      a node identifying a particular bank account. In OWL<a href=
      "#OWL">[OWL]</a> terms, if <code>bank:accountNumber</code> is
      an <code>owl:InverseFunctionalProperty</code>, then the node
      must be the <code>owl:sameAs</code> any other node with the
      same account number. In that case, the patch will be strong.
    </p>
    <p>
      If, however, many accounts can have the same number, applying
      that patch to another knowledge base may inadvertently alter
      the wrong account. The patch would be weak.
    </p>
    <p>
      In normal information processing, of course, numbers such as
      bank account numbers are used to avoid this confusion.
      Consider those graphs in which every blank node is in fact
      unambiguously identified by one functional or inverse
      functional property. Further, that property is invariant
      under any changes represented by the deltas.
    </p>
    <p>
      The pattern for terms goes as follows:
    </p>
    <p class="definition">
      Given a background ontology <samp>W</samp> and a graph
      <samp>G</samp>, if a blank node <samp>b</samp> in
      <samp>G</samp> is the object of a triple whose subject
      <samp>v</samp> is <em>functionally ground</em> and whose
      predicate <samp>p</samp> is an
      <code>owl:FunctionalProperty</code> according to
      <samp>W</samp>, then <samp>v.p</samp> is a <em>functional
      term label</em> for <samp>b</samp> in <samp>G</samp> with
      respect to <samp>W</samp>. Likewise, <samp>v\uparrow q</samp>
      is a functional term label for <samp>b</samp> if
      <samp>q</samp> is an
      <code>owl:InverseFunctionalProperty</code>, b is the subject,
      and v is the object. Recursively, v is functionally ground if
      it is a name (URI or literal) or a bnode with a functional
      term label.
    </p>
    <p>
      Then we can rewrite certain graphs:
    </p>
    <p class="definition">
      With respect to a background ontology <samp>W</samp>, a graph
      <samp>G</samp> is <em>fully labeled</em> iff every node in
      <samp>G</samp> is functionally ground. A <em>functional RDF
      graph</em> is a set of triples whose terms are URIs,
      literals, or functional terms. A functional RDF graph
      <samp>F</samp> is a <em>functional analog</em> of an RDF
      graph <samp>G</samp> iff <samp>G</samp> is fully labeled and
      <samp>F</samp> can be obtained from <samp>G</samp> by
      replacing each bnode b in <samp>G</samp> with a functional
      term label for b.
    </p>
    <p>
      The diffs of functional RDF graphs are just as simple to make
      as ground RDF deltas:
    </p>
    <p class="definition">
      Given a background ontology <samp>W</samp>, a <em>strong</em>
      delta between fully labeled graphs <samp>G1</samp> and
      <samp>G2</samp> is a pair <samp>(insertions,
      deletions)</samp> where <samp>insertions</samp> is the set
      difference <samp>F2-F1</samp>, deletions is
      <samp>F1-F2</samp>, and <samp>F1</samp> and <samp>F2</samp>
      are functional analogs of <samp>G1</samp> and <samp>G2</samp>
      respectively.
    </p>
    <p class="online">
      (@@need to define sigma for strong deltas?) It is actually
      the same as for any delta: horn match and delete or insert.
    </p>
    <p>
      A strong delta is like a context diff that cannot be
      mis-applied.
    </p>
    <p class="proposition">
      If <samp>D</samp> is a strong delta between fully labeled
      graphs <samp>k1</samp> and <samp>k2</samp>, and
      <samp>k3</samp> is a subset of <samp>k1</samp>, then
      <samp>\Sigma(k3, D)</samp> is consistent with
      <samp>k2</samp>. <span class="online">@@TODO: proof</span>
    </p>
    <p>
      One advantage of a strong patch is, then, that one can take a
      patch from any true knowledge base change and apply it to a
      subset knowledge base, and the result will be true. For
      example, if changes to a knowledge base are represented by a
      sequence of strong diffs, one can subscribe to the diffs from
      any given point on, and acquire a subset of the final
      knowledge base.
    </p>
    <p>
      As a practical matter, achieving fully labeled graphs
      requires care in building and using the ontology. As a
      supplement to the good practice of using URIs to distributing
      data, it is useful to identify things indirectly by using
      terms with published ontologies that say whether they are
      many-many, many-1, 1-many or 1-1. The <a href=
      "/2000/10/swap/diff.py">diff.py</a> program from <a href=
      "/2000/10/swap/Overview.html">SWAP</a> will generate a strong
      diff between two files, provided it can find sufficient
      information in the Web to fully label the input graphs.
    </p>
    <p class="online">
      We note in passing that the ontologies we used all involved
      inverse functional datatype properties, which are OWL/Full
      but not OWL/DL.
    </p>
    <h2>
      Application to Update and Sync
    </h2>
    <p>
      Though we have made small scale tests, we are interested in
      pursuing strong diffs, and suspect they will be are useful in
      a variety of applications.
    </p>
    <h3>
      Peer-peer update and sync
    </h3>
    <p>
      The algorithm for synchronizing two databases can be
      straightforwardly generalized to N. In a decentralized
      peer-peer network such as Network News Transfer
      Protocol<a href="#NNTP">[NNTP]</a> (or many others), messages
      are timestamped and distributed eventually to every party,
      though a message may be received by different parties at
      different times. When the network is reliable, there may be a
      well-defined maximum delivery time.
    </p>
    <p>
      A crude algorithm is to apply the patches in order of the
      time-stamp. If a message arrives with a timestamp preceding
      the recent ones already taken into account, they are unwound
      so that the new version can be built in the proper order. A
      patch which fails (as in a CVS conflict) is rejected. In the
      case of RDF graphs, failure can be a pre-agreed form of
      consistency, such as (for example) OWL-DL consistency. The
      sender of the failed patch will realize this as they will be
      running the same algorithm on the same patches, and will have
      to take recovery action.
    </p>
    <p>
      A new version can be given a version id by hashing the
      version id of its predecessor with the message id of the
      patch used to make the new from the old. The community can
      refer to versions by these ids, and if they want to refer to
      a commonly held document, then one only has to wait for the
      maximum delivery time to know that everyone in the community
      will know the value of the knowledge base for that version.
      Even without waiting, anyone who knows of a version with that
      ID will know they have the same contents.
    </p>
    <h3>
      Patches as knowledge
    </h3>
    <p>
      The idea of the strong patch file format is interesting
      because a patch is a little bit of knowledge. A patch for
      example that where my phone number was 1234 it should now be
      5678, when in the context in which it is known to be a change
      to a valid knowledge base between one week and the next,
      indicates that my phone number has actually changed. One
      might conclude, say, that I moved or changed jobs. A strong
      patch has meaning in itself, and distributing and filtering
      these becomes an interesting way of processing knowledge. In
      some areas (like houses for sale) it is the new changed
      information which is of most interest, and in some areas
      (like currency rates) if you listen to a stream of changes
      you will in fact accumulate a working knowledge of the area.
    </p>
    <h3>
      Patches as news
    </h3>
    <p>
      From the historical <em>NCSA Mosaic What's New</em> page to
      the current syndication of RSS streams <a href=
      "#RSS">[RSS]</a>, the interest in news on (or off) the Web
      demonstrates that there is great interest in changes to the
      status quo. We speculate that this will also be the case on
      the Semantic Web. When the state is represented in RDF, then
      RDF diffs represent news. The W3C Technical Reports list is
      available as RDF, and the W3C RSS feed is partly,
      effectively, a list of changes to the Tech Reports list. This
      could be formalized by explicitly distributing RDF diffs.
    </p>
    <h2>
      Future directions
    </h2>
    <p>
      The algorithm developed to date produces difference files
      only on graphs which are labeled directly with URIs or
      indirectly with functional properties or inverse functional
      properties.
    </p>
    <p>
      It may be useful to extend the algorithm to cope with graphs
      which are not completely labeled, but where the unlabeled
      bits are the same in each graph, and so a strong diff can
      still be produced. Another avenue would be to look at using
      more than one property to label a node when one is not
      sufficient.
    </p>
    <p>
      Applications which do not need robustness can use weak
      patches. The algorithm could be extended to do more of a
      canonicalization-style signature-based match to optionally
      give a weak diff where a strong diff cannot be given.
    </p>
    <p class="online">
      In practice, while RDF fundamentally has a graph structure,
      the graph is often used to encode ordered lists (RDF
      collections). While lists are in fact represented by a
      structure of <em>first</em> and <em>rest</em> links within
      the graph, when serialized they are normally represented
      directly as lists, and within software implementations they
      may be stored specially. The representation of changes to
      lists may merit a special syntax in the difference file, to
      avoid a mess of <em>rdf:first</em> and <em>rest:rest</em>
      statements. (@@DanC: first/rest are functional, so I don't
      think this case mertis anything special.)
    </p>
    <p>
      RDF does not contain the notion of an unordered set, though
      one can with OWL create a class which has an enumerated set
      of members. If the use of unordered sets becomes common,
      which the authors suspect would be wise in the long run, then
      a difference engine should be aware of such sets and be able
      to express differences between them.
    </p>
    <p>
      This application, like the rule language, demonstrates the
      usefulness of the quoted formulae of n3. The authors believe
      that many applications will need this ability to quote RDF
      graphs within graphs. As n3 becomes a language of
      communication, difference files will of course have to
      express changes to nested formulae. As these are graphs, this
      is basically a straightforward recursive use of the
      difference system for single graphs. A simple though verbose
      alternative is to reify the n3 before building differences.
    </p>
    <p>
      With these extensions, the simple difference file format may
      lose the elegance of its current simplicity. However, even
      with these extensions, most data and ontologies shipped
      around the web -- the bottom layers of the semantic web layer
      cake -- will be plain RDF graphs and so have simple
      difference files.
    </p>
    <p>
      Clearly there are many algorithms which can be imagined for
      efficiently generating deltas for RDF graphs. The ones
      written are not particularly efficient, having being designed
      as proof of concept.
    </p>
    <h2>
      Conclusions
    </h2>
    <p>
      There are many uses for technology of communicating
      differences between graphs or changes to a graph. While in
      general the generation of differences is basically a graph
      isomorphism problem, in a wide set of practical cases, one
      can efficiently generate a difference, or patch file.
      So-called strong patch files are particularly interesting,
      and open up a new series of applications based on the
      syndication of change information. However, to be able to
      generate them, one needs either a well-labeled graph, which
      in turn needs an ontological knowledge of inverse functional
      properties to allow nodes to be indirectly labeled. The patch
      file format proposed is simple, being a new ontology of only
      two (or three) new properties, and directly uses Notation3
      syntax and semantics, which itself is a simple extension of
      RDF. This format can be generated by all sorts of
      difference-finding algorithms. It can be absorbed by any
      system capable of matching RDF subgraphs. The patch file
      ontology is a candidate for a future standard for remote
      update of RDF data.
    </p>
    <div>
      <h2>
        References
      </h2>
      <p class="online">
        see <a href="lncs04/Diffbib.bib">Diffbib.bib</a>
      </p>
      <dl class="bib">
        <dt class="misc">
          [<a name="RDF04" id="RDF04">RDF04</a>]
        </dt>
        <dd>
          <span class="author">Beckett, D.</span> <cite><a href=
          "http://www.w3.org/TR/2004/REC-rdf-syntax-grammar-20040210/">
          RDF/XML Syntax Specification (Revised)</a></cite>
          <span class="institution">W3C</span> <span class=
          "type">Recommendation</span>, 10 <span class=
          "month">February</span> <span class="year">2004</span>.
          <p class="online">
            <a href=
            "http://www.w3.org/TR/rdf-syntax-grammar">Latest
            version</a> available at
            <code>http://www.w3.org/TR/rdf-syntax-grammar</code>
          </p>
        </dd>
        <dt class="misc">
          [<a name="DC02" id="DC02">DC02</a>]
        </dt>
        <dd>
          <span class="author">Beckett, D. and Miller, E. and
          Brickley, D.</span> <a href=
          "http://dublincore.org/documents/2002/07/31/dcmes-xml/"><cite>
          Expressing Simple Dublin Core in RDF/XML</cite></a>
          <span class="institution">Dublin Core Metadata
          Initiative</span> <span class=
          "type">Recommendation</span> 31 <span class=
          "month">July</span> <span class="year">2002</span>
        </dd>
        <dt class="misc">
          [<a name="RSS" id="RSS">RSS</a>]
        </dt>
        <dd>
          <span class="author">Beged-Dov, Gabe et. al.</span>
          <cite><a href="http://web.resource.org/rss/1.0/">RDF Site
          Summary (RSS) 1.0</a></cite> 6 <span class=
          "month">December</span> <span class="year">2000</span>
        </dd>
        <dt class="inproceedings">
          [<a name="Ber90" id="Ber90">Ber90</a>]
        </dt>
        <dd>
          <span class="author">Berliner, Brian</span> <cite>CVS II:
          Parallelizing Software Development</cite> <span class=
          "booktitle"><a href="http://www.usenix.org/">USENIX</a>
          Conference Proceedings</span> pp <span class=
          "pages">341--352</span> <span class=
          "month">January</span> 22-26, <span class=
          "year">1990</span> <span class="address">Washington,
          D.C.</span>
          <p class="online">
            <a href=
            "http://www.hpcc.ecs.soton.ac.uk/hpci/tools/cvs/html/cvs-paper.html">
            online copy</a>; <a href=
            "http://cvsweb.xfree86.org/cvsweb/cvs/doc/cvs-paper.ms">
            ms source</a>
          </p>
        </dd>
        <dt class="misc">
          [<a name="Ber03" id="Ber03">Ber03</a>]
        </dt>
        <dd>
          <span class="author">Berners-Lee, Tim and Hawke, Sandro
          and Connolly, Dan</span> <cite><a href=
          "http://www.w3.org/2000/10/swap/doc/">Semantic Web
          Tutorial Using N3</a></cite> <span class=
          "howpublished">Twelfth International World Wide Web
          Conference</span> <span class="address">Budapest,
          Hungary</span> <span class="month">May</span>
          <span class="year">2003</span>
        </dd>
        <dt class="techreport">
          [<a name="Car03" id="Car03">Car03</a>]
        </dt>
        <dd>
          <span class="author">Carroll, Jeremy J. and Dickinson,
          Ian and Dollin, Chris and Reynolds, Dave and Seaborne,
          Andy and Wilkinson, Kevin</span> <cite><a href=
          "http://www.hpl.hp.com/techreports/2003/HPL-2003-146.html">
          Jena: Implementing the Semantic Web
          Recommendations</a></cite> <span class=
          "institution">Hewlett-Packard</span> <span class=
          "number">HPL-2003-146</span> <span class=
          "month">Dec</span> <span class="year">2003</span>
          <p class="online">
            <a href=
            "http://www.hpl.hp.com/semweb/jena.htm">Jena</a>
            includes a graph diff program <code>rdfcompare</code>
            in the <a href=
            "http://jena.sourceforge.net/tools.html">command line
            tools</a>.
          </p>
        </dd>
        <dt class="TechReport">
          [<a name="Car03s" id="Car03s">Car03s</a>]
        </dt>
        <dd>
          <span class="author">Caroll, Jeremy J.</span>
          <cite><a href=
          "http://www.hpl.hp.com/techreports/2003/HPL-2003-142.html">
          Signing RDF Graphs</a></cite> <span class=
          "institution">Hewlett-Packard</span> <span class=
          "number">HPL-2003-142</span> <span class=
          "month">Jul</span> <span class="year">2003</span>
        </dd>
        <dt class="Article">
          [<a name="Codd70" id="Codd70">Codd70</a>]
        </dt>
        <dd>
          <span class="author">Codd, E. F.</span> <cite><a href=
          "http://www.acm.org/classics/nov95/">A Relational Model
          of Data for Large Shared Data Banks</a></cite>,
          <span class="journal">Communications of the ACM</span>,
          Vol. <span class="volume">13</span>, No. <span class=
          "number">6</span>, <span class="month">June</span>
          <span class="year">1970</span>, pp. <span class=
          "pages">377--387</span>.
        </dd>
        <dt class="Article">
          [<a name="Gol03" id="Gol03">Gol03</a>]
        </dt>
        <dd>
          <span class="author">Golbeck, Jennifer and Fragoso,
          Gilberto and Hartel, Frank and Hendler, James and Parsia,
          Bijan and Oberthaler, Jim</span> <cite><a href=
          "http://www.mindswap.org/papers/WebSemantics-NCI.pdf">The
          national cancer institute's thesaurus and
          ontology</a></cite>. <span class="journal">Journal of Web
          Semantics</span>, <span class=
          "volume">1</span>(<span class="number">1</span>),
          <span class="month">Dec</span> <span class=
          "year">2003</span>.
        </dd>
        <dt class="misc">
          [<a name="RDFT04" id="RDFT04">RDFT04</a>]
        </dt>
        <dd>
          <span class="author">Grant, J. and Beckett, D.</span>
          <cite><a href=
          "http://www.w3.org/TR/2004/REC-rdf-testcases-20040210/">RDF
          Test Cases</a></cite>, <span class=
          "institution">W3C</span> <span class=
          "type">Recommendation</span>, 10 <span class=
          "month">February</span> <span class="year">2004</span>.
          <p class="online">
            <a href="http://www.w3.org/TR/rdf-testcases">Latest
            version</a> available at
            <tt>http://www.w3.org/TR/rdf-testcases</tt>
          </p>
        </dd>
        <dt class="misc">
          [<a name="RDFC04" id="RDFC04">RDFC04</a>]
        </dt>
        <dd>
          <span class="author">Klyne, G. and Carroll, J. J.</span>
          <cite><a href=
          "http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/">Resource
          Description Framework (RDF): Concepts and Abstract
          Syntax</a></cite>, <span class="institution">W3C</span>
          <span class="type">Recommendation</span>, 10 <span class=
          "month">February</span> <span class="year">2004</span>.
          <p class="online">
            <a href="http://www.w3.org/TR/rdf-concepts/">Latest
            version</a> available at
            <code>http://www.w3.org/TR/rdf-concepts/</code>
          </p>
        </dd>
        <dt class="TechReport">
          [<a name="NNTP" id="NNTP">NNTP</a>]
        </dt>
        <dd>
          <span class="author">Kantor, Brian and Lapsley,
          Phil</span> <cite><a href=
          "http://www.ietf.org/rfc/rfc977">Network News Transfer
          Protocol</a></cite> <span class="institution">IETF</span>
          <span class="number">RFC977</span> <span class=
          "month">February</span> <span class="year">1986</span>
        </dd>
        <dt class="misc">
          [<a name="Kly04" id="Kly04">Kly04</a>]
        </dt>
        <dd>
          <span class="author">Klyne, Graham</span> <cite><a href=
          "http://www.ninebynine.org/RDFNotes/Swish/Intro.html">Semantic
          Web Inference Scripting in Haskell</a></cite>
          <span class="month">Feb</span> <span class=
          "year">2004</span>
          <p class="online">
            see esp. section <a href=
            "http://www.ninebynine.org/RDFNotes/Swish/Intro.html#GraphDiff">
            Comparing graphs</a>
          </p>
        </dd>
        <dt class="Book">
          [<a name="Kob93" id="Kob93">Kob93</a>]
        </dt>
        <dd>
          <span class="author">Johannes K<span title=
          "\&quot;o">&ouml;</span>bler and Uwe Sch<span title=
          "\&quot;o">&ouml;</span>ning and Jacobo Tor<span title=
          "\'a">&aacute;</span>n</span> <cite><a href=
          "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3680-3">The
          Graph Isomorphism Problem: Its Structural
          Complexity</a></cite> <span class="series">Progress in
          Theoretical Computer Science</span>. <span class=
          "publisher">Birkh<span title=
          "\&quot;a">&auml;</span>user</span>, <span class=
          "address">Boston, MA</span>, (<span class=
          "year">1993</span>).
          <p class="online">
            <a href=
            "http://www.informatik.hu-berlin.de/Institut/struktur/algorithmenII/Buecher/GI/">
            preface, TOC, etc.</a>. cited in <a href=
            "http://www.math.tu-berlin.de/~schwartz/papers/KaibelSchwartz2002.references.bib">
            KaibelSchwartz2002.references.bib</a>
          </p>
        </dd>
        <dt class="Article">
          [<a name="Mill85" id="Mill85">Mill85</a>]
        </dt>
        <dd>
          <span class="author">Miller, Webb and Myers, Eugene
          W.</span> <cite>A File Comparison Program</cite>
          <span class="journal">Software---Practice and
          Experience</span>, <span class=
          "volume">15</span>(<span class="number">11</span>), pp.
          <span class="pages">1025--1040</span>, <span class=
          "month">November</span> <span class="year">1985</span>.
          <p class="online">
            <a href=
            "http://liinwww.ira.uka.de/cgi-bin/bibshow?e=TF0tqf/fyqboefe%7d789658&amp;r=bibtex&amp;mode=intra">
            bib</a>
          </p>
        </dd>
        <dt class="Book">
          [<a name="Ski97" id="Ski97">Ski97</a>]
        </dt>
        <dd>
          <span class="author">Skiena, Steve</span> <cite>The
          Algorithm Design Manual</cite> <span class=
          "publisher"><a href="http://www.telospub.com/">Telos
          Pr</a></span> <span class="address">New York</span>
          <span class="year">1997</span>
        </dd>
        <dt class="incollection">
          [<a name="Ski01" id="Ski01">Ski01</a>]
        </dt>
        <dd>
          <span class="author"><a href=
          "http://www.cs.sunysb.edu/~skiena/">Skiena,
          Steve</a></span> <span class="chapter">1.5.9</span>
          <cite><a href=
          "http://www.cs.sunysb.edu/~algorith/files/graph-isomorphism.shtml">
          Graph Isomorphism</a></cite> in the <span class=
          "booktitle"><a href=
          "http://www.cs.sunysb.edu/~algorith/index.html">Stony
          Brook Algorithm Repository</a></span> <span class=
          "publisher">Stony Brook University</span> <span class=
          "year">2001</span>
          <p class="online">
            with reference to <a href=
            "http://www.cs.sunysb.edu/~algorith/implement/gmt/implement.shtml">
            GMT - Graph Matching Toolkit</a>
          </p>
        </dd>
        <dt class="Article">
          [<a name="Tich85" id="Tich85">Tich85</a>]
        </dt>
        <dd>
          <span class="author">Tichy, W.</span> <a href=
          "http://portal.acm.org/citation.cfm?id=4202&amp;dl=ACM&amp;coll=GUIDE">
          <cite>RCS--a system for version control</cite></a>
          <span class="journal">Software Practice <span class=
          "amp">&amp;</span> Experience</span> Volume <span class=
          "volume">15</span> , Issue <span class="number">7</span>
          (<span class="month">July</span> <span class=
          "year">1985</span>) Pages: <span class=
          "pages">637--654</span>
        </dd>
        <dt class="misc">
          [<a name="Sync02" id="Sync02">Sync02</a>]
        </dt>
        <dd>
          <cite><a href=
          "http://www.openmobilealliance.org/tech/affiliates/syncml/syncmlindex.html">
          SyncML Specifications, Version 1.1</a></cite>
          <span class="month">Feb</span> <span class=
          "year">2002</span> <span class="publisher"><a href=
          "http://www.openmobilealliance.org/">Open Mobile Alliance
          (OMA)</a></span>
        </dd>
        <dt class="misc">
          [<a name="Wall" id="Wall">Wall</a>]
        </dt>
        <dd>
          <span class="author">Wall, Larry et. al.</span>
          <cite><a href=
          "http://www.gnu.org/software/patch/patch.html">patch</a></cite>
          <span class="publisher">Free Software Foundation</span>
          27 <span class="month">Jun</span> <span class=
          "year">2000</span>
        </dd>
        <dt class="misc">
          [<a name="EARL" id="EARL">EARL</a>]
        </dt>
        <dd>
          <span class="author">Chisholm, W. and Palmer, S.
          B.</span> Editors: <cite><a href=
          "http://www.w3.org/TR/2002/WD-EARL10-20021206/">Evaluation
          and Report Language (EARL) 1.0</a></cite> <span class=
          "institution">W3C</span> <span class="type">Working
          Draft</span> (work in progress), 6 <span class=
          "month">December</span> <span class="year">2002</span>
          <p class="online">
            <a href="http://www.w3.org/TR/EARL10/">Latest
            version</a> available at http://www.w3.org/TR/EARL10/
          </p>
        </dd>
        <dt class="misc">
          [<a name="OWLT" id="OWLT">OWLT</a>]
        </dt>
        <dd>
          <span class="author">Carroll, J. J. and De Roo, J.</span>
          Editors: <cite><a href=
          "http://www.w3.org/TR/2004/REC-owl-test-20040210/">OWL
          Web Ontology Language Test Cases</a></cite> <span class=
          "institution">W3C</span> <span class=
          "type">Recommendation</span> , 10 <span class=
          "month">February</span> <span class="year">2004</span>.
          <p class="online">
            <a href="http://www.w3.org/TR/owl-test/">Latest
            version</a> available at http://www.w3.org/TR/owl-test/
          </p>
        </dd>
        <dt class="misc">
          [<a name="OWL" id="OWL">OWL</a>]
        </dt>
        <dd>
          <span class="author">Schreiber, G. and Dean, M.</span>
          Editors: <cite><a href=
          "http://www.w3.org/TR/2004/REC-owl-ref-20040210/">OWL Web
          Ontology Language Reference</a></cite> <span class=
          "institution">W3C</span> <span class=
          "type">Recommendation</span> , 10 <span class=
          "month">February</span> <span class="year">2004</span>.
          <p class="online">
            <a href="http://www.w3.org/TR/owl-ref/">Latest
            version</a> available at http://www.w3.org/TR/owl-ref/
          </p>
        </dd>
      </dl>
    </div>
    <hr />
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      <a href="Overview.html">Up to Design Issues</a>
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