>Kathy and Pat,
>I agree with Pat's explanation, but I think it could be made
>somewhat clearer by distinguishing the base domain D from
>the domain D' of *all* relations over D for second-order logic
>(and then a domain D'' of *all* relations over D', etc.).
>PH> The key semantic difference between the other logics is
> > that they all impose conditions on the domain, requiring
> > it to contain some entities as a result of containing others.
> > So for example, classical second-order logic semantics
> > requires that the domain is contain all relations
> > over the base domain.
>I would rephrase the last sentence in the following way:
> So for example, classical second-order logic semantics
> starts with the given base domain D and introduces
> another domain D' of *all* relations over D. (01)
That is closer to the usual formulation, and
probably clearer, yes. And it is that extended
domain D' which the second-order quantifiers
range over. (02)
>I just wanted to give different names D, D', D'', etc.
>to distinguish the base domain D from any domains that
>may be introduced by implicit assumptions.
>CL allows the domain D to contain relations, but it doesn't
>require D to contain *all possible* relations. (03)
or indeed any relations, if you want to exclude
them: CL has the notion of a 'segregated dialect'
to allow for this textbook first-order case. (04)
>Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
>Shared Files: http://ontolog.cim3.net/file/
>Community Wiki: http://ontolog.cim3.net/wiki/
>To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
IHMC (850)434 8903 or (650)494 3973 home
40 South Alcaniz St. (850)202 4416 office
Pensacola (850)202 4440 fax
FL 32502 (850)291 0667 cell
phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes (07)
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (08)