[sc34wg3] TR: comment - RDFTM: Survey of Interoperability Proposals

[Murray Altheim]

Lars Marius Garshol wrote:
> * Robert Barta
> | 
> | But then we realized that a sound mathematical model [1] allows you
> | to define operations on topic maps and build - based on these
> | operations - query and constraint languages.
> 
> Clearly that's good, but it's not what Patel-Schneider is asking for,
> if I understand him correctly. He wants a *logic* model, not just a
> mathematical one. So I guess \Tau won't make much difference in that
> regard.

How are you differentiating "logic" and "mathematical" as regards
models?

Quoting the RDF Semantics document by Pat Hayes that Patel-Schneider
is touting as providing what he needs:

  "This document uses a basic technique called model theory for
   specifying the semantics of a formal language. [...] Model
   theory assumes that the language refers to a 'world', and
   describes the minimal conditions that a world must satisfy
   in order to assign an appropriate meaning for every
   expression in the language. A particular world is called an
   interpretation, so that model theory might be better called
   'interpretation theory'. The idea is to provide an abstract,
   mathematical account of the properties that any such
   interpretation must have, making as few assumptions as
   possible about its actual nature or intrinsic structure,
   thereby retaining as much generality as possible. The chief
   utility of a formal semantic theory is not to provide any deep
   analysis of the nature of the things being described by the
   language or to suggest any particular processing model, but
   rather to provide a technical way to determine when inference
   processes are valid, i.e. when they preserve truth. This
   provides the maximal freedom for implementations while
   preserving a globally coherent notion of meaning.

   Model theory tries to be metaphysically and ontologically
   neutral. It is typically couched in the language of set
   theory simply because that is the normal language of
   mathematics - for example, this semantics assumes that
   names denote things in a set IR called the 'universe' -
   but the use of set-theoretic language here is not supposed
   to imply that the things in the universe are set-theoretic
   in nature. Model theory is usually most relevant to
   implementation via the notion of entailment, described
   later, which makes it possible to define valid inference
   rules."
               -- from the "Introduction" in RDF Semantics [1]

It is the field of mathematical logic (including set theory
and others) that provides the tools by which we may create
model theories. I think this is simply Robert (and myself,
for that matter) being colloquial in our use of language,
not any inherent failing on the part of his model (or "model
theory," to be more exacting) to provide the necessary basis,
so I hardly think it fair to so quickly dismiss Robert's work
as not fulfilling Patel-Schneider's putative requirements.

Murray

[1] RDF Semantics, W3C Recommendation 10 February 2004, Pat Hayes, ed.
     http://www.w3.org/TR/rdf-mt/#prelim
......................................................................
Murray Altheim                    http://kmi.open.ac.uk/people/murray/
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK               .

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