Re: SUO: Model theory for modal logics
At 23:15 -0400 9/08/2003, John F. Sowa wrote:
>I don't believe that it is possible to overstate the need
>for reasoning about multiple modalities.
agreed
> In natural
>languages, people freely intermix multiple modal operators
>in the same sentence, but Kripke semantics makes it very
>difficult to support more than one kind of modality.
Now we know this is not true. Plenty of multi-modal logics (for
Kripke frames) have been developed during the 90s and in several
cases they have nice formal properties.
A good source is the forthcoming book by Dov Gabbay, Agi Kurucz,
Frank Wolter, and Michael Zakharyaschev "Many-dimensional modal
logics: theory and applications", Elsevier Science, 2003.
The results are quite surprising when you compare them to what was
known in the 70s or 80s.
>For all these reasons, I believe that the metaphor of laws,
>facts, and contexts suggests more promising directions for
>future research than the metaphor of possible worlds.
It might help. But I agree with you and Chris, better keep in mind
that these are just metaphors.
Btw, the problem is not with the term law only. It won't take long
before somebody asks what a "fact" is in this approach and why we can
have different sets of facts and why a set of facts has to be
maximally consistent...
Stefano