Kathy and Pat, (01)
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.). (02)
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. (03)
I would rephrase the last sentence in the following way: (04)
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. (05)
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. (06)
CL allows the domain D to contain relations, but it doesn't
require D to contain *all possible* relations. (07)
John (08)
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