On Oct 27, 2009, at 4:56 PM, Matthew West wrote:
> Dear Ian,
>
>> PS - IDEAS is higher order,
>
> MW: Actually it probably isn't. You would need to get someone like
> Chris
> Menzel to explain, but having classes with members that are classes
> that
> have members that are individuals is apparently not enough to make it
> higher order. If I understood correctly this is because you can do a
> transformation into a first order form,... (01)
That is correct. To be genuinely higher-order requires an additional
semantic constraint on the number of classes there are in the domains
of the higher-order quantifiers. Absent that constraint, "higher-
order" interpretations can be transformed into first-order. But it's
hard to know exactly because IDEAS appears to be a box and arrow
language with lots of evocative labels ("Thing", "Individual", "Type",
"PowerType", ...) but no semantics. That they have powertypes in
particular is suggestive of full higher-order logic, but again it's
just a label without a semantics, so there is no way to know. (02)
>> and extensional. It's founding categories are individual (something
>> with spatio-temporal extent), type and tuple. I can see how CL
>> handles type and tuple (albeit through some arcane notion,
>
> MW: CL is an abstract syntax. (03)
With a rigorous semantics. (04)
> The concrete syntaxes actually include a graphical notation -
> conceptual graphs. (05)
Exactly correct. (06)
> If you chose, you could probably map the ideas notation to the CL
> abstract syntax, or a subset of it. (07)
So long as the syntax of the notation is well-defined and it has a
clear semantics, you surely could. (08)
>> probably starting with "for all..."), but it doesn't seem to have a
>> fundamental category of something with spatio-temporal extent.
>
> MW: It does not have to. It just has not made that commitment, and
> should not either, CL is a language not an ontology. It does not
> prevent you from declaring that there are individuals that are
> spatio-temporal extents. (09)
Again, exactly correct. (010)
>> As that's the criterion on which the entire ontology is founded, I
>> think I'd rather use a notation that is also founded on this
>> principle.
>
> MW: Well the advantage of that for you is that you will be able to
> make convenient diagrams. The disadvantage is that no-one who is not
> a 4 dimensionalist will want to use your notation. (011)
Indeed. (012)
>> Maybe we just built the right wheel for what we're doing, instead
>> of re-inventing one.
>
> MW: Well if it's a graphical notation, chances are it's just boxes
> and lines again. (013)
That's all I've found, but perhaps there is a rigorous semantics for
it lurking somewhere. (014)
Chris Menzel (015)
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