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\title{A Pragmatic Theory of Reference for the Web}
\numberofauthors{1}
\author{
\alignauthor Dan Connolly\\
 \affaddr{MIT Computer Science and Artificial Intelligence Laboratory (CSAIL)}
}
\maketitle
\label{firstpage}
  




\par The World Wide Web is a ``global information universe''\cite{BL92}. Links are used to represent
all sorts of subtle, rich, and and even ambiguous references.
One one web page, we might find...

\begin{verbatim}
I saw a great <a
href="http://www.imdb.com/title/tt0091605/"
>movie starring Sean Connery</a>
\end{verbatim}


\par ... while another says...

\begin{verbatim}
The <a
href="http://www.imdb.com/title/tt0091605/"
>IMDB page on "The Name of the Rose"</a>
is a great source of information.
\end{verbatim}


\par Meanwhile, the Web Architecture document\cite{webarch} says, ``By design a URI identifies one
resource.'' Which does \url{ http://www.imdb.com/title/tt0091605/} identify, then,
the movie, or the page about the movie? The pragmatic answer is: it
doesn't matter that much, provided the community of people making the
links and serving the information ``agree (to a reasonable extent) on
a set of terms and their meanings.''


\par Human readers are quite robust when it comes to understanding puns
and ambiguously indirect references, but computers are not; in a C
program, the difference between {\tt *p} and {\tt **p} is the
difference between a useful computational result and a crash.  Even
for human readers, there are limits.  If visiting
\url{ http://www.imdb.com/name/nm0000225/} with a web browser showed
Christian Slater's photo and filmography, and a writer used that
address to refer, indirectly, to Sean Connery, readers would likely
feel that \empty Grice's Maxim of
Manner\cite{Gr89}, ``Avoid ambiguity'', had been
violated.


\par The design of the Web of documents we have today is the result of
taking the simplest features of hypertext designs from 15 to 20 years
ago, adding globally scoped Uniform Resource Identifiers (URIs), and
relaxing link consistency constraints. The social dynamics of the Web
include lots of people agreeing to just a few design constraints in
order to get a significant return on their investment, whether from
reading or writing or both.


\par By analogy, the Semantic Web involves starting with simple database
and logic designs and using URIs for column names and symbol
terms. Which constraints need relaxing and which social norms will
result in exponential growth are still open questions.


\par The W3C Technical Architecture Group (\empty TAG) is chartered to ``document
and build consensus around principles of Web architecture''.  This
paper gives a pragmatic theory of reference in the form of some
principles established by the W3C TAG and some personal
conjectures about issues that are still open.

\section{An analysis of httpRange-14}
  


\par One of the most intensely debated TAG issues is \empty httpRange-14:
What is the range of the HTTP dereference function?. The dicussion
of the issue is almost all publicly recorded, but following it is
challenging, not only because of the quantity, but because of the
diverse backgrounds of the participants, leading to much
miscommunication.


\par Perhaps a formal analysis is an effective way to
summarize. For example, the simple logical statement that
\url{ http://purl.org/dc/elements/1.1/title} is an
{\tt rdf:Property} was a matter of some dispute.


\par The Dublin Core Metadata Initiative (\empty DCMI) publishes a schema\footnote{
\url{ http://purl.org/dc/elements/1.1/}}
that says:

\begin{verbatim}
<rdf:Property
  rdf:about="http://purl.org/dc/elements/1.1/title">
  <rdfs:label xml:lang="en-US"
  >Title</rdfs:label>
  <!-- ... details elided ... -->
</rdf:Property>
\end{verbatim}


\par Or, equivalently, using turtle\cite{ttl} notation:

\begin{verbatim}
@prefix rdf:
  <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.
@prefix rdfs:
  <http://www.w3.org/2000/01/rdf-schema#> .
@prefix dc:
  <http://purl.org/dc/elements/1.1/>.

dc:title rdf:type rdf:Property.
\end{verbatim}


\par Meanwhile, Tim Berners-Lee argued that ``HTTP URIs (without {\tt \#})
should be understood as referring to documents, not cars''.  To
formalize this position, we'll use some string manipulation properties
from N3\cite{swtut2003} and set aside the
prohibition against literal subjects, going just beyond turtle into
N3. Also, we use the {\tt log:uri} property, which is similar to
the {\tt name} quoting function in KIF\cite{kif}.

\begin{verbatim}
@prefix dc:
  <http://purl.org/dc/elements/1.1/>.
@prefix log:
  <http://www.w3.org/2000/10/swap/log#> .
@prefix str:
  <http://www.w3.org/2000/10/swap/string#> .

dc:title
  log:uri "http://purl.org/dc/elements/1.1/title".
"http://purl.org/dc/elements/1.1/title"
  str:startsWith "http:".
"http://purl.org/dc/elements/1.1/title"
  str:notMatches "#".
\end{verbatim}


\par We can use OWL\cite{owl} to formalize that something is
a document and not a car, once we choose, for the purpose of this
discussion, URIs for the concepts of documents and cars:

\begin{verbatim}
@prefix owl:
  <http://www.w3.org/2002/07/owl#>.
@prefix tbl:
  <http://example/tbl-terms#>.

tbl:Document owl:disjointFrom tbl:Car.
\end{verbatim}


\par Berners-Lee also argued that properties are not documents:

\begin{verbatim}
tbl:Document
  owl:disjointFrom tbl:Car, rdf:Property.
\end{verbatim}


\par To state his position generally, we add an N3 rule:

\begin{verbatim}
tbl:Document
  owl:disjointFrom tbl:Car, rdf:Property.

{
 ?X log:uri [
   str:startsWith "http:";
   str:notMatches "#"
 ] }
 => { ?X a tbl:Document }.
\end{verbatim}


\par This position is quite clearly inconsistent with the DCMI schema.
Berners-Lee was unable to persuade a critical mass of the TAG to
accept this position.  The utility of the dublin core vocabulary was
apparent and the argument against its use of hashless HTTP URIs
included few practical consequences. Plus, the constraint seems to
encroach on the very important principle of opacity of URIs.  Any
general-purpose algorithm for finding out the nature of a resource
starting from only its URI is a constraint on how URIs are
minted. 


\par Further, Mark Baker asserted the right to assign any meaning at all
to URIs that he owns. In particular, he said that
\url{ http://markbaker.ca/} denotes his very self. To capture this
position, we will borrow from the FOAF\cite{foafintro} vocabulary:

\begin{verbatim}
<http://markbaker.ca/>
  a foaf:Person;
  foaf:name "Mark Baker".
\end{verbatim}


\par This is also inconsistent with Berners-Lee's position, since
Berners-Lee held that {\tt foaf:Person} is disjoint with
{\tt tbl:Document}.


\par Meanwhile, the DCMI showed some willingness to cooperate with those
who hold that RDF Properties and web pages are disjoint; they arranged
for \empty HTTP
redirections \cite{RFC2616}, rather than \empty 200
OK repsonses, in reply to GET requests to
\url{ http://purl.org/dc/elements/1.1/title}.


\par Let's introduce some terms for discussing the HTTP protocol. To
dereference \url{ http://site.example/path}, it's typical to
make a TCP connection to port 80 of {\tt site.example} and
send a {\tt GET /path} request. If the reply is...

\begin{verbatim}
200 OK
content-type: text/plain

hello world.
\end{verbatim}


\par Then we'll say that:

\begin{verbatim}
@prefix http:
  <http://example/http-terms#>.
@prefix mime:
  <http://example/mime-terms#>.

_:reply1 a http:OKResponse;
  http:about <http://site.example/path>;
  mime:body "hello world.";
  mime:content-type "text/plain".
\end{verbatim}


\par It is stipulated by all parties in the httpRange-14 discussion that
in this case, the {\tt hello world.} body of type
{\tt text/plain} is a {\em representation} of
\url{ http://site.example/path}. We can state the general rule as:

\begin{verbatim}
@prefix w:
  <http://example/webarch-terms#>.

{
_:m a http:OKResponse;
  http:about ?R;
  mime:body ?BYTES;
  mime:content-type ?TYPE.
} => {
?R w:representation [
  mime:content-type ?TYPE;
  mime:body ?BYTES ].
}
\end{verbatim}


\par When asked if {\tt tbl:Document} included the targets
of http POST messages, Berners-Lee said yes, and agreed, to
some extent that the that the term {\em document} is misleading.
The TAG coined the term {\em \empty Information Resource}. The
term is not completely defined, but the 15 Jun 2005 decision
of the TAG to address httpRange-14 says:


    \begin{quote}
  

\par The TAG provides advice to the community that they may mint {\tt http} URIs for any resource provided that they follow this simple rule for the sake of removing ambiguity:
\begin{itemize}
  \item If an {\tt http} resource responds to a GET request with a 2xx response, then the resource identified by that URI is an information resource;\item If an {\tt http} resource responds to a GET request with a 303 (See Other) response, then the resource identified by that URI could be any resource;\item If an {\tt http} resource responds to a GET request with a 4xx (error) response, then the nature of the resource is unknown.
    \end{itemize}
  

    \end{quote}
  


\par We can state this formally as:

\begin{verbatim}
{
?M a http:OKResponse;
  http:about ?R.
} => { ?R a w:InformationResource }.
\end{verbatim}


\par We consider it implicit in this decision that it applies to the
case of a dereferencing an {\tt ftp:} URI as well, so the following
single triple states the position of the TAG quite concisely with
respect to the terminology developed so far:

\begin{verbatim}
w:representation
  rdfs:domain w:InformationResource.
\end{verbatim}


\par Since DCMI does {\em not} claim that {\tt dc:title} is a
{\tt w:InformationResource}, Berners-Lee is able to endorse
their claim that {\tt dc:title} is an {\tt rdf:Property} (for
example, in his tabulator implementation, announced in \cite{tabu}) while maintaining his position that
{\tt rdf:Property} is disjoint from
{\tt w:InformationResource}.


\par Note that the TAG has not taken a position on whether
{\tt w:InformationResource} intersects with
{\tt rdf:Property}.They do say, ``Other things, such as cars and
dogs [...] are resources too. They are not information resources,
however [...]'' which strongly suggests that 
{\tt w:InformationResource} is disjoint with
{\tt foaf:Person}. Since Mark Baker's
server responds with ordinary 200 OK replies when asked about
\url{ http://markbaker.ca/}, we have:

\begin{verbatim}
<http://markbaker.ca/>
  a w:InformationResource.

foaf:Person owl:disjointWith w:InformationResource.
\end{verbatim}


\par So we are have an inconsisitency between the definition of
{\tt w:InformationResource} and Mark Baker's claim that \url{ http://markbaker.ca/} is a {\tt foaf:Person}.
While ``anyone can say anything about anything''\cite{RDFC}, there are consequences to making disagreeable
claims.



\section{The value of agreement}
  


\par Consider a formalized movie database, where a request to GET
\url{ http://fmdb.example/title/tt0091605/} gives:

\begin{verbatim}
<#title0091605>
  dc:title "The Name of the Rose";
  film:rating 7.7;
  film:star <#nm0000225>.

<#nm0000225>
  dca:agentName "Christian Slater".
\end{verbatim}


\par And suppose John Doe wants a widely-understood identifier for
Christian Slater so that he can use it in a description of a photo
that Jim took of Christian. Jim writes, in
\url{ http://photohost.example/jim/photo20.ttl}:

\begin{verbatim}
<photo20>
  dc:title "Smile, Christian!";
  foaf:depicts
   <http://fmdb.example/title/tt0091605/#nm0000225>.
\end{verbatim}


\par Clearly, then, a SPARQL query\cite{SPARQL} over
the merge of those documents of the form...

\begin{verbatim}
SELECT ?photo, ?name
WHERE  {
 ?photo foaf:depicts [
   dca:agentName ?name
 ]
}
\end{verbatim}


\par ...will return:
\begin{center}\begin{tabular}{|c|c|}
\hline
{\bf photo}&\url{ <http://photohost.example/jim/photo20>}\tabularnewline
\hline
{\bf name}&{\tt "Christian Slater"}\tabularnewline
\hline
\end{tabular}
\end{center}



\par But suppose, meanwhile, that Jim does not think The Name of
the Rose merits 7.7 out of 10 stars. A SPARQL query over
the same merge of those documents of the form...
\begin{verbatim}
SELECT ?photo ?title ?rating
WHERE {
 ?photo foaf:depicts _:who.
 [] dc:title ?title;
    film:star _:who;
    film:rating ?rating
}
\end{verbatim}


\par ...will return:
\begin{center}\begin{tabular}{|c|c|}
\hline
{\bf photo}&\url{ <http://photohost.example/jim/photo20>}\tabularnewline
\hline
{\bf title}&{\tt "The Name of the Rose"}\tabularnewline
\hline
{\bf rating}&{\tt 7.7}\tabularnewline
\hline
\end{tabular}
\end{center}



\par How can Jim reuse the information such as the name of the person
depicted in his photo without implyling that the movie merits 7.7 out
of 10 stars? One approach is to not merge the sources, but rather
treat the fmdb data as a separate graph in the SPARQL dataset.
The photo subject's name can be computed using a more explicit query:

\begin{verbatim}
SELECT
FROM <http://photohost.example/jim/photo20.ttl>
FROM NAMED <http://fmdb.example/title/tt0091605/>
 ?photo, ?name WHERE
  { ?photo foaf:depicts ?who.
    GRAPH <http://fmdb.example/title/tt0091605/> {
      ?who dca:agentName ?name }.
  }
\end{verbatim}


\par This approach is akin to lifting between contexts\cite{G91}. It is a workable apprach to integrating data
from separate contexts, but it is clearly not as straightforward as
merging. The cost of keeping contexts separate demonstrates that
{\em agreement is valuable}.  The providers of
{\tt fmdb.example} can lower Jim's cost to use their information if
they publish film ratings that Jim agrees with.


\section{Delegation, consent and causal chains}
  \label{s42}



\par Jim could, of course, make up his own URI for the subject of his
photo. But then Jim would have to maintain the information about the
actor's name, the movies he starred in, and their titles, at his own
cost. And if others in Jim's position did likewise, consumers of all
this data would be able to correlate photo subjects only at a
significant cost of dealing with {\em \empty URI
aliases}. We conjecture that overall utility for the community is
maximized if we adopt a {\em \empty causal
theory of reference}\cite{Kr80}. In particular:

\begin{enumerate}
  \item To mint a term in the community, choose a URI of the form
{\tt doc\#id} and publish at doc
some information that motivates others to use the term in
a manner that is consistent with your intended meaning(s).

\item Use of a URI of the form.
{\tt doc\#id} implies agreement
to information published at {\tt doc}.
    \end{enumerate}
  


\par Justification of this conjecture is in progress\cite{Co06}, using terms such
as {\em intent} and {\em impact} from the \empty TAG
discussion of extensibility and versioning in Edinburgh in
September 2005.



\section{Advice: Use hash URIs for properties and classes}
  


\par If you want to write RDF schemas that are consistent with the TAG's
position on httpRange-14, you have three options:
\begin{enumerate}
  \item Use the {\tt doc\#id} pattern as above.\item Set up HTTP redirects a la {\tt dc:title}.\item Populate the intersection of {\tt w:InformationResource}
with {\tt rdf:Property}.

    \end{enumerate}
  


\par The third option is like publishing movie reviews that people
disagree with. The second option is more trouble than the first,
unless the vocabulary you're describing is very large. So I advise
the first option.

\subsection{Fragments as sections vs. people}
  


\par Some argue that ``Using {\tt \#} [in this way] makes it impossible to
make assertions about parts of documents (e.g. Person A authored
Section \#3).''\cite{A04}. Indeed, this
is a concern. Let's consider it formally, using FRBR\cite{frbr}, \cite{iflafrbr}.  Suppose
\url{ http://fansite.example/baseball} is a little database of great
baseball players, with some statistics on
\url{ http://fansite.example/baseball\#FredPatek}, among others:

\begin{verbatim}
@prefix foaf:
  <http://xmlns.com/foaf/0.1/>.
@prefix baseball:
  <http://fansite.example/baseball#>.

baseball:average
  rdfs:domain foaf:Person.

baseball:FredPatek
  baseball:average 0.250 .
\end{verbatim}


\par These data might be published in RDF/XML:

\begin{verbatim}
    <foaf:Person rdf:ID="FredPatek">
        <baseball:average
          rdf:datatype=
    "http://www.w3.org/2001/XMLSchema#decimal"
          >0.25</baseball:average>
    </foaf:Person>
\end{verbatim}


\par And then someone might use the ID to say that the Fred Patek section was
written by somebody named John Doe:

\begin{verbatim}
@prefix frbr:
   <http://purl.org/vocab/frbr/core#>.

<http://fansite.example/baseball#FredPatek>
 frbr:creator [ foaf:name "John Doe" ].
\end{verbatim}


\par These two are inconsistent, since the domain of
{\tt frbr:creator} is {\tt frbr:Work}, which is disjoint with
{\tt foaf:Person}, the domain of {\tt baseball:average}.


\par So indeed, if we choose URIs of the form {\tt doc\#id} for
people, it leads to inconsistencies with quite reasonable ontologies
if we also use them as document section identifiers. I advise authors
to choose one or the other for each fragment identifier they publish
and be consistent.


\par In order for this to work with documents published both in RDF/XML
and XHTML, the XHTML media type specifications may need to be ammended
so that authors can ``opt out'' of the section-of-the-document meaning
of fragment identifiers that they publish. For example, the
{\tt profile} attribute from section \empty 7.4.4.3
Meta data profiles of the HTML 4 specification\cite{HTML4} seems like a reasonable opt-out signal.


\par Populating the intersection of {\tt w:InformationResource}
with {\tt foaf:Person}, the way Mark Baker seems to, seems likely
to conflict with useful and reasonable ontologies.  I suggest adopting
{\tt w:InformationResource rdfs:subClassOf frbr:Work} as a
practical constraint. The {\tt foaf:primaryTopic} relationship
seems particularly useful for relating web pages to things. Rather
than..

\begin{verbatim}
<http://markbaker.ca/> a foaf:Person;
foaf:name "Mark Baker"\end{verbatim}


\par ... I suggest:

\begin{verbatim}
<http://markbaker.ca/> foaf:primaryTopic
  [ foaf:Person; foaf:name "Mark Baker"].
\end{verbatim}




\section{Conclusions and Future Work}
  


\par While the theory presented here gives little by way of rigorously
justified theorems, we hope it gives a coherent and pragmatic approach
to nagivating many issues of identity and reference in the Web.


\par We hope the formal analysis of the httpRange-14 discussion and
decision, down to a single RDF triple, makes the issue clear without
distorting the positions that it summarizes.  We also hope it
demonstrates the utility of RDF, turtle, and N3 as analytic
tools.


\par The
justification of the causal theory of reference is ongoing work. See,
for example, Berners-Lee's \empty Total Cost of
Ontologies (TCO) argument in his \empty ISWC 2005
presentation.


\par When considering which constraints need relaxing and which social
norms will result in exponential growth of the Semantic Web,
mechanisms for expressing trust seem to be critical. We are exploring
approaches using quoting a la ``if \url{ http://weather.example/ny}
contains a formula of the form {\tt <ny\#weather> nws:temp ?X}
then lift that claim, {\tt <ny\#weather> nws:temp ?X} into the
knowledge base as a fact.'' We are exploring these quoting techniques
along with digital signature and proof exchange as a general-purpose
trust infrastructure. These explorations suggest that the law of the
excluded middle, i.e that every formula is either true or false,
should be relaxed in order to allow \empty indirect
self-reference. Constructive proofs seem more promising than those
that use classical fist order reasoning\cite{Co06b}.





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