Re: Semantics, in particular DAML+OIL semantics

Guha,

I have some questions about what you call "special interpretations"
the logical symbols.

Are logical symbols the symbols for connectives, along with quantifiers?

Wouldn't MA treat these symbols the same way as MB does?

It makes sense to me that for the _nonlogical_ vocabulary
(constant symbols, function symbols, and relation symbols),
MA and MB can provide different interpretations.

But I am puzzled by how MA or MB might treat the logical symbols differently.

Can you explain?

Thanks,

Jim


On Mon, 12 Aug 2002, R.V.Guha wrote:

> 
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> Please let me clarify. What I am saying is the following.<br>
> <br>
> Assume we have language A, with model theory MA. Expressions in A are assigned
> satisfying interpretations by MA. In particular, MA will provide special
> interpretations for some of the symbols in A. These are the logical symbols
> of A.<br>
> <br>
> Next, we have language B, with model theory MB. Expressions in B are assigned
> satisfying interpretations by MB. In particular, MB will provide special
> interpretations for some of the symbols in B. These are the logical symbols
> of B.<br>
> <br>
> Now, further imagine that the surface syntax of A and B are identical to
> a point where wffs of A are also wffs of B and vice versa, except, since
> the logical symbols of A and B are different, MA and MB assign different
> interpretations to to these wffs. Of course, depending on whether the expression
> uses only the logical symbols of A or B, one can say that the "correct" model
> theory is MA or MB respectively. Now what if we get an expression that uses
> logical symbols from A and B? There is no more a sense of the "correct" model
> theory.<br>
> <br>
> The solution is to map both model theories into a more general model theory
> (where "general model theory" is a very precisely defined concept) and appeal
> to that theory. <br>
> <br>
> This is exactly the situation we are facing with RDF, RDFS, OWL, DAML-S ...<br>
> <br>
> guha<br>
> <br>
> <br>
> <br>
> <br>
> Enrico Franconi wrote:<br>
> <blockquote type="cite"
>  cite="mid15703.62976.940060.709468@gramsci.cs.man.ac.uk">
>   <pre wrap="">On August 12, R.V.Guha writes:
>   </pre>
>   <blockquote type="cite">
>     <pre wrap="">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. 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".
>     </pre>
>   </blockquote>
>   <pre wrap=""><!---->
> I don't really see why model theories do have this limitation. In
> fact, you say:
> 
>   </pre>
>   <blockquote type="cite">
>     <pre wrap="">Fortunately, since the whole semantics game grounds out in 
> interpretations, I believe we can have a formal model of what it means 
> for these two approaches to say the same thing. 
>     </pre>
>   </blockquote>
>   <pre wrap=""><!---->
> The definition of valid interpretations is what a model theory is
> about. So, please enlighten us why if languages are defined through
> model theoretic semantics it is then impossible to define the
> semantics of some combination of them.
> 
> cheers
> -- e.
> 
> Enrico Franconi                     - <a class="moz-txt-link-abbreviated" href="mailto:franconi@inf.unibz.it">franconi@inf.unibz.it</a>
> Free University of Bozen-Bolzano    - <a class="moz-txt-link-freetext" href="http://www.inf.unibz.it/~franconi/">http://www.inf.unibz.it/~franconi/</a>
> Faculty of Computer Science         - Phone: (+39) 0471-315-642
> I-39100 Bozen-Bolzano BZ, Italy     - Fax:   (+39) 0471-315-649
>   </pre>
> </blockquote>
> <br>
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> 
>

Received on Monday, 12 August 2002 15:57:47 UTC