Just to restate this again, as it frequently gets lost: (01)
[Chris Menzel]
> It strikes me that it might be best to play down the idea of a
> lattice of theories/ontologies. The idea — induced simply by the
> fact that, for any two theories, one is a subset of the other or not
> (in which case the theories are not on a common branch of the
> lattice) — is meant only as a helpful image (I think John himself
> agrees), not as anything implementable (not that Leo is suggesting
> otherwise). (02)
I for one would be more than a little sad if this idea gets played
down to much. (03)
We are *implementing* and *using* something that looks very
much like 'the lattice of theories'. Of course, the relations/lines
in the lattice [the 'development graph' in CASL/HETS]
are not simple subset relations, but
show dependencies between axioms, theories, outstanding
and already satisfied proof obligations and inter-theory
morphisms, etc. --- but they *look* like a lattice and
so the lattice may offer the metaphor that is
the the easiest to understand. This
seems important to me in that it provides
a way of breaking into the single monolithic view of
ontologies that prevents re-use and agreement on
inter-relationships. (04)
This kind of large-scale structuring used with CASL
is something that could equally well be applied to
CL; Till would probably be happy to say something
about this more technically. (05)
>
> CM> So it strikes me that it might be best to play down the lattice
>> of theories, both because it is arguably too coarse and also
>> because too many folks seize upon the image and think it buys
>> something practical. (06)
In our opinion, the use of structured connections between
structured theories certainly buys something practical.
(Well, it offers something practical, we have to convince
others to do the buying I expect :-) (07)
Best,
John.
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