A Functional Philosophy of the Web

Harry Halpin, <H.Halpin@ed.ac.uk>

Textorized Parthenon

Ph.D. Proposal, Edinburgh, April 2006

Introduction

Thesis

A philosophical analysis of the Web that relies on the construal of information and a definition of informational knowledge as public and explicit information leads to a solid theoretical framework for Web Architecture: The Web is moving from a universal information space to a universal computation space

If this is implemented computationally, we can use the Semantic Web as an ``open world'' type system for this framework, in particular XML processing.

Note

This notion of information also undermine traditional notions of the individual as an ontological category.

Approach

We're going to have use an interdisciplinary approach from two rarely connected fields: philosophy and the World Wide Web.

Philosophy of Computation? The Web?

Are computers (including the Web) a valid subject matter of philosophy?

Is "Philosophy of the Mind" valid?

In this sense, the term "embodied" is a lexical band-aid covering a 350-year-old wound generated and kept suppurating by a schizoid metaphysics. M. Sheets-Johnstone

Why the Web? Why not philosophy of unicorns? Or Kings of France?

The Web is crucially important, unlike unicorns.

More Objections: Neural Salvationism (Churchlands), Consciousness First! (Searle), Reduction to Physics, Reduction to Mathematics

Tim Berner's Lee (in)famous Semantic Web Stack

TimBL's Semantic Web Service Stack Picture

Not so fast...

httpRange-14: Everything Must Have a URI?

The Eiffel Tower versus a web-page about the Eiffel Tower: Isn't there something fundamentally different? And what URI do you use for the Eiffel Tower qua Eiffel Tower?

The Symbol Grounding Problem?

Eiffel Tower Homepage

Eiffel Tower Picture

The URI of the web-page is clearly http://www.tour-eiffel.fr/.

The largest difference between AI and the Semantic Web is the use of URIs

The TAG definitions...

Information Resource

The distinguishing characteristic of these resources is that all of their essential characteristics can be conveyed in a message(Jacobs and Walsh, 2005)

Non-Information Resource?

Other things, such as cars and dogs (and, if you've printed this document on physical sheets of paper, the artifact that you are holding in your hand), are resources too. They are not information resources, however, because their essence is not information. Although it is possible to describe a great many things about a car or a dog in a sequence of bits, the sum of those things will invariably be an approximation of the essential character of the resource. (Jacobs and Walsh, 2005)

Using Shannon's Information Theory

Information Theory Picture

Two Problems

The Epistemological Assumption

The use of "knowledge" or "certainty" to define whether or not a sender has received a message, and exactly what they received.

The Metaphysical Assumption

The sender and receiver are discrete individuals (although not necessarily different, as it can be the same individual spread out over time)

Philosophical Reconstruction

A stack of philosophical and formal analysis for Web architecture

Harry's Philosophy Stack

The Epistemological Problem

Information is defined implicitly in terms of knowledge, an expensive notion.

What is Knowledge?

Since Plato knowledge has often been defined as justified true belief. It is unclear what justified means, and this definitions fall victim to the Gettier problems (Gettier, 1963).

We should get away from the thorny problem of "knowledge."

Dretkse's Theory of Information

Dretske's Semantic Theory of Information

Information is portable, modular, public, and about something (i.e. has a meaning or interpretation).

Key Observation: Telling someone how many bits they have does not tell them what information was transmitted.

Dretske's Definition of Information Content:

"A signal r carries the information that s is F iff the conditional probability of s's being F, given r and k is 1 (where k is the knowledge of the receiver)" (Dretske, 1981).

Dretske's Definition of Knowledge:

Information causally sustaining a belief (Dretkse, 1981).

Aren't these circular?

Informational Knowledge

Public

As being part and parcel of information, it has to be capable of being shared, and therefore "public."

Useful

Knowledge enables the possessor of the knowledge to commit a successful action. The definition of "success" is a dynamic norm rooted in the "cascade of Darwinian Algorithms" (Dennett, 2002) - related to neo-Fregean or Davidsonian notions of truth (Luntley, 1999).

Explicit

The information specifies to the possessor completely how to commit the successful action, i.e. a constructivist or algorithmic approach.

The Return of Representationalism

Just when dynamicism and anti-represenationalism had won...

Just as we enter the age of embodiment in cognitive science, the Web is leading our lives to be increasingly disembodied.

Good Old Fashioned AI in the form of knowledge representation is back on the Web.


Ian Horrocks Pat Hayes Jim Hendler

What are Representations?

Haugeland states that the mark of a representation is the standing-in relationship (Haugeland, 1991).

Representations as Explanations: Bechtel argues that any amount of covariance that is enough to give the possibility of a stand-in representation (Bechtel, 1998)

Representations as physically implemented structures: create local effects that are effective by virtue of their correspondence with non-local parts of the world.

Correspondece is accomplished by having the raw material of the representation having some temporal contact with the target, which leads a structural correspondance (Smith, 1996).

Representations can be compositional.

Extended Mind and External Representations

We remain agnostic about whether there are internal representations

Yet there definitely are external representations, which may not be secondary case, but may in fact be the primary case.

Thus the ability to " deal with the visscitudes and vagarities of earthly existence" via perfect digital memory and precise computation (Haugeland, 1991).

Via the Extended Mind Hypothesis these external, digital representations are just as cognitive as any internal ones (Clark and Chalmers, 1998).

The Web provides a universal place to access representations.

As latency decreases, it may not be so disembodied after all.

Back to the Web:

The difference between non-information resources and information resources is that information resources are representational.

However, we cannot define the meaning of a resource by itself, since any Web-mandated direct object theory of reference will be hopelessly ambiguous (Kripke, 1971).

Reference versus access.

Instead, we should define a the meaning of a resource to be its interpretation in context to its formal model theory, its links to the rest of the Web, and any available information given by access to the URI itself.

The interpretation is the successful use of the resource in its context.

Yet given any XML or HTML document, we don't know how to use it!

But it's a Mess!

Too many standards - too little coherence

Picture of Too Many Standards

XML and Knowledge

XML without a description of its processing is not fully describing

By embedding the minimal number of constructs in XML we can extend XML into functional processing language, that uses the Semantic Web as a type system and can access Web Services.

Therefore we can place useful, explicit, and algorithmic knowledge on the Web in documents themselves.

Inside the XML Document

Thompson showed how you can put the processing instructions inside the XML document (2005).
<page xmlns:fx="http://www.ltg.ed.ac.uk/~ht/functionalXML">
  <fx:transform xmlns:xi="http://www.w3.org/2001/XInclude"
              stylesheet="xmlhtmlout.xsl">
    <fx:validate schemaDocument="someschema.xsd">
      <document version="2.0">
        <head profile="http://www.w3.org/2003/g/data-view">
          <link rel="transformation"
            href="http://www.example.org/xml2rdf.xsl" />
        </head>
        <body>
          <title>Some Document</title>
            <author = "Brian Suda" />
          <title>
            My input data is below!
          </title>
          <data>
            The <b>data itself</b>!
          </data>
        </body>
      </document>
    </fx:validate>
  </fx:transform>

From the Semantic Web...

The Semantic Web enables a number of different logics to be shared in a standard format (Berners-Lee et. al., 2001).

Due to its unique constraints (the open-world problem in particular) currently it supports mostly RDF, which is a semantic network formalism with a formal semantics, and OWL, which has two description logic families.

However, like all knowledge it has the essential problem of procedural attachment: ontologies can only describe non-temporal information .

Also, people aren't serializing their data using the Semantic Web.

The Semantic Web is a solution in search of a problem.

We believe that problem could be describing computations on the Web.

RDF as a Typing System

If XML is data, then can the Semantic Web provide types for that data?

On the Web it may be important that a string is a firstName as in ``the first name of a person,'' and not just any string.

Explicitly model the world semantics of your data, not just give them data types.

<fx:let xmlns:sfx="http://www.ibiblio.org/hhalpin/sfXML"
        xmlns:storeOnt="http://www.example.org/StoreOntology/"  >
  <sfx:bind name="myPerson" type="storeOnt:StoreCustomer">
         <fx:include href="customerOrder121.xml" />
  </sfx:bind>

Semantic Web Services Made Simple

If the Semantic Web is open-world typing, and Web Services are functions available on the Web, then Semantic Web Services are typed functions for the Web.

Invoke Web Services not just by their URI, but by the type of information they output and input (Sirin et. al., 2004).

All we require is that WSDL inputs and outputs can be annotated with RDF - just like SAWSDL.

Example

<body>
  <fx:let xmlns:fx="http://www.ibiblio.org/hhalpin/sfXML"
        xmlns:dirOnt="http://www.example.org/DirectionsOntology/">
    <sfx:bind name="myAddress" type="dirOnt:Address">
      <sfx:include href="myaddr.rdf"/>
    </sfx:bind> 
    <sfx:bind name="yourAddress" type="dirOnt:Address">
      <sfx:include href="your_addr.rdf"/>
    </sfx:bind>
    <h1>Welcome to My Web Page</h1>
    <p>The <b>directions</b> to my House are here:</p>
    <sfx:defun name="doDir">
      <sfx:lambda type="dirOnt:Directions">
        <sfx:args>
          <sfx:arg name="origin" type="dirOnt:Origin"/>
          <sfx:arg name="destination" type="dirOnt:Destination"/>
        </sfx:args>
      </sfx:lambda>
    </sfx:defun>
    <sfx:defun name="doMap">
      <sfx:lambda outputType="dirOnt:Map">
        <sfx:args>
          <sfx:arg name="address" type="dirOnt:Location"/>
        </sfx:args>
      </sfx:lambda>  
    </sfx:defun>
    <sfx:apply name="doDir" origin="$yourAddress" destination="$myAddress" />
    <p>You may find this <b>map</b> useful as well!</p>
    <sfx:apply name="doMap" address="$myAddress"/>
  </fx:let>
</body>

Proofs for XML Processing

Curry-Howard Isomorphism = Proofs are Programs

Typed Functional Programming Languages = Intuitionistic Predicate Logic (Thompson, 2001)

Example Proof
<fx:let xmlns:fx="http://www.ltg.ed.ac.uk/~ht/functionalXML">
  <fx:bind name="myvariable">
    <fx:include href="document.xml"/>
  </fx:bind>
  <fx:cond>
    <fx:case test="$myvariable/document/@version &gt; 1.0">
      <fx:transform stylesheet="http://www.example.com/xhtmlout.xsd">
         <fx:authenticate stylesheet="http://www.me.com/key.gpg.asc">
           <fx:include href="$myvariable"/>
         </fx:authenticate>
      </fx:transform>
    </fx:case>
  </fx:cond>
</fx:let>

A Quick Glance at the Metaphysical Assumption

Our characterization of information presumes individuals (Strawson, 1959) . This is an expensive notion to be assuming, so it would be preferable if we could define individuals in terms of information.

Even within psychology or philosophy what counts as an individual is not always clear.

.

A way out: Use an autopoietic notion of the individual as self-sustaining feedback cycles (Maturana and Varela, 1973). The feedback cycles can then be defined as information flows.

The View from Nowhere

This is increasingly looking like classical artificial intelligence - a disembodied brain:

Brain in the Sky

Yet this seemed not to model intelligence - yet it does do justice to some of the characteristics of computers. Yet the Web is about humans and computers.

Keeping It Down

Lately intelligence is viewed as an embodied robot:

Cute Little Robot

Yet does this really work to explain the Web, that seems to lead to the growth of representations and disembodiment? Walking robots are hard, but not interesting from an augmentation standpoint - after all, we already walk.

Metaphysical Solution

Both visions also base on their theorization of the notion of the individual, be it a robotic dog or a disembodied intelligence.

Yet intelligence is seen in networks of information flows (such as that between an individual and their environment). So - where's the individual?

The Web, by decreasing the latency between information flows and providing a universal space for information storage with a perfect digital memory, provides the perfect compliment for normally weak human representational powers, increasing utility for all involved.

This increased representational and computational power also increases human communicative power.

Conclusions

Is this a unified picture?

From information (Old-Fashioned Web) to knowledge and logic (Semantic Web) to typed functions (Semantic Web Services).

Technical Claim:Concretely, the idea of Semantic Web Services as typed functions provides a better model than current competitors like BPEL or modelling solutions such as OWL-S. Typed functions over a universal digital information space provides a universal model of computation - and that's all the Web is - a large computer.

Analysis in a Nutshell:By catching our concepts back up to our technology we can therefore re-formulate the notions of information, knowledge, representation, digitality, truth, and individuality along the way...and help the Semantic Web not repeat some of the classical problems of AI.

Wrapping Up

Any questions?

References:

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