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Face-to-Face: Reading and Outline for "SWOL Discussion"

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Fri, 04 Jan 2002 15:10:20 -0500
To: www-webont-wg@w3.org
Message-Id: <20020104151020Q.pfps@research.bell-labs.com>

	Face-to-face SWOL Reading List and Discussion Outline

Annotated Reading List:

1/ Pat Hayes' model theory for RDF
   Most important here is the Introduction section that gives a good, short
   description of how model theory works.

2/ DAML+OIL model theory
   DAML+OIL is syntax-compatible with RDF(S), but not
   semantics-compatible.  Further, this model theory would not provide an
   appropriate entailment relationship.

3/ OWL definition - RDF compatible
	swol.text (4 January 2002)
   This definition of OWL is semantics-compatible with RDF(S), but not
   syntax-compatible.  The syntax is given in terms of the XQuery data
   model (http://www.w3.org/TR/2001/query-datamodel/), but the only real
   difference from XML Infosets is that the XQuery data model includes XML
   Schema typing information.

4/ OWL' definition - XML compatible with partial RDF compatability
	swol-xml-rdf.text  (3 January 2002)
   This definition of OWL is neither syntax- nor semantics-compatible with
   RDF(S) in general.  However, for base facts it is both syntax- and
   semantics-compatible with RDF.  It is much simpler than the initial OWL

Presentation Outline:

What is a representation formalism?
- a formal system that has a well-defined meaning
- designed to represent something about the world
- e.g., relational data bases, propositional logic, first-order logic,
	modal logic, Montague logic, description logics

Why do representation formalisms need a well-defined meaning?
- after all people cope without, don't they?
  - well, they sort of cope, and their repair mechanisms are complex
- lack of well-defined meaning leads to misunderstanding between communicants

Horror stories
- range and domain in RDFS
- lists, bags, and alternatives in RDF
- reification in RDF
- QUA (East coast vs. West coast) in KL-ONE
- C++ (vs ML or FORTRAN)

How is meaning defined?
- data models - don't work for more-expressive formalisms
- proof theory 
  - specify what syntactic structures follow from (are derivable from) others
- model theory 
  - specify which states of the world are compatible with syntactic structures
  - syntactic structures follow from (are entailed by) others if they are
    compatible all the syntactic structures that the others are compatible with
- axiomatization
  - provides a mapping to some other formalism that (hopefully) has a
    well-defined meaning
- can relate proof theories with model theories
  - sound proof theory - does not produce non-entailed formulae
  - complete proof theory - produces all entailed formulae

Benefits of standard methods for providing meaning
- proof theory - can be mechanized
- model theory - intuitive way to provide meaning
	       - allows for various proof theories

Pitfalls in formal systems
- conflict with intuitions - e.g., prescriptive vs descriptive
			   - e.g., DAML+OIL entailment
- inconsistency - e.g., set theory
		- e.g., Liar's paradox

Issues in the design of a Web Ontology Language
- what syntax to use
  - XML
  - RDF graphs
- how to specify semantics
  - model theory vs proof theory
  - NB: axiomatization is parasitic
- how much expressive power is needed
- what computational properties are wanted
- what computational properties result

A simple Web Ontology Language (OWL')
- syntax basics
  - datatypes
  - knowledge bases
  - descriptions
  - class definitions
  - property definitions
  - statements
- interpretations
- semantic conditions
- entailment  

Proposed Approaches

   - RDF syntax
   - semantic extension of RDF
   - problem - entailment not correct
     - example - AND [Person Student] vs AND [Student Person]
   - possible solution - require all lists (and other syntactic structures)
		         in all interpretations
   - problem - potential inconsistency

2/ OWL (4 January 2002)
   - XML syntax, relatively compatible with RDF
   - semantic extension of RDF, includes RDF meta theory
   - problem - complex constructs - e.g., conditional transitivity
   - possible solution - forbid such conditional constructs
   - problem - unprincipled

3/ OWL' (3 January 2002)
   - XML syntax, object stuff in RDF
   - semantics different from RDF

Tricky Points

- generating syntax - lists, classes, etc.
- self reference

Received on Friday, 4 January 2002 15:11:55 UTC

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