Re: Semantics, in particular DAML+OIL semantics

From: "R.V.Guha" <guha@guha.com>
Subject: Re: Semantics, in particular DAML+OIL semantics
Date: Mon, 12 Aug 2002 10:15:41 -0700

> Ian, thank for posting these to rdf-logic. It would be good to have a 
> discussion on the issue of different approaches to providing a semantics 
> for the languages of the semantic web.
> 
> I agree with you that for the purpose of providing a semantics for any 
> one particular language, a "native" model theory, i.e., one that maps 
> sets of expressions in that language to satisfying interpretations, is 
> best in terms of perspicuity and pedagogy. So, I agree that it is 
> important that RDF, OWL, ... be given native model theories.
> 
> I would however argue that in the context of the Semantic Web, we are 
> dealing with a situation that is quite different from when we are 
> developing a single, standalone language. We are developing a set of 
> languages, that are supposed to work together, i.e., wffs on the SW may 
> include constructs from multiple of these languages. More so, these 
> languages are expected to be layered on top of each other. Now, one can 
> argue, as some have, that this charter is ill-conc[ei]ved, but for the 
> purpose of this email, I will assume that as a given. 

[Hmm.  This is not the way I understand the charter under which the Web
 Ontology Working Group is working.  The Web Ontology Working Group is
 constrained to use wffs only from RDF, i.e., n-triples.]

> Further, I am also 
> not going to get into a discussion of whether RDF/OWL should include 
> certain features. That is the topic of another email.
> 
> The problem, in this context, with relying solely on model theories, is 
> that this does not give us a tool for providing a semantics for 
> expressions that mix constructs from  different languages. 

Why not?  What prevents a logic from having several syntaxes and building a
model theory for it?  (In essence what is happening is that the
syntax for the logic is the combination of the several syntaxes.  This
combination can even allow for expressions that have sub-expressions from
more than one of the sub-syntaxes.)

In fact, in an ideal world it should have been possible to build an
integrated model theory for XML, XML Schema, RDF, RDF Schema, and OWL, each
with their own syntax.  As far as I can see the main reason that this
doesn't work is that XML and RDF have different notions of what
interpretations should be built on (ordered node-labelled trees vs
unordered node- and edge-labelled directed graphs).

> That is a 
> rather severe limitation of relying solely on model theories.  Axiomatic 
> approaches on the other hand, by mapping everything into a common 
> language, do enable us to provide a semantics for such "mixed expressions".

I fail to see how axiomatic approaches are any more liberating than
model-theoretic approaches or proof-theoretic approaches in this regard.

In fact, an axiomatic approach limits one to the facilities of a particular
target logic.  An axiomatization into first-order logic limits the source
logics to the power of first-order logic, preventing, for example,
transitive closure from being part of any source logic.  Axiomatization
without translation also limits the source logics to one particular
syntax.  Axiomatization with translation introduces another source of
complexity to the mix.

Model-theoretic approaches instead allow the source logics to expand beyond
the reach of any one particular logic.  Of course, each expansion requires
work to expand the model theory, but then the axiomatic approach also
requires work to produce the axiomatization.

> I am not advocating that we abandon model theoretic approaches in favour 
> of the other approach. I would like to see both. Which of course brings 
> us to the issue of making sure that both are saying the same thing. 
> Fortunately, since the whole semantics game grounds out in 
> interpretations, 

I believe that there are other schools of thought that do not ground out in
interpretations but instead are based on notions of consequence.

> I believe we can have a formal model of what it means 
> for these two approaches to say the same thing. Pat Hayes and I have 
> taken a stab at this in our Lbase document.

The LBase document assumes that the model theory for a particular logic is
a restriction of the model theory for Lbase.  This is quite constraining.

> I look forward to your reactions.

Well, I, for one, remain confused as to the benefits of the LBase
approach.   I don't see it having any significant implementation benefits.
I don't see it having any significant expository benefits.

> thank you
> 
> Guha

Peter F. Patel-Schneider
Bell Labs Research

Received on Tuesday, 13 August 2002 13:58:23 UTC