Re: Semantics, in particular DAML+OIL semantics

On August 12, R.V.Guha writes:
> 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.
> 
> 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.

I completely agree with you.
But this is not what you were saying in the previous post:

> 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".

It appears to me that your "general model theory" is exactly what you
need. So, there is definitely something you want to tell us about the
advantage of axiomatic approaches to combine logics which I don't get.

cheers
-- e.

Enrico Franconi                     - franconi@inf.unibz.it
Free University of Bozen-Bolzano    - http://www.inf.unibz.it/~franconi/
Faculty of Computer Science         - Phone: (+39) 0471-315-642
I-39100 Bozen-Bolzano BZ, Italy     - Fax:   (+39) 0471-315-649

Received on Monday, 12 August 2002 18:26:00 UTC