RE: SUO: RE: A proposed SUO content outline
Dear Pat,
<snip>
> > > >
> > > > >
> > > > > Status
> > > > >
> > > > > Contains axioms and relations that apply to all classes that
> > > > > are characteristics or qualities that is described by
> discrete,
> > > > > unordered values.
> > > >
> > > >I agree that this is an important category, and it is also a
> > > gap in the
> > > >current version of the merged ontology.
> > >
> > > I have no clear idea what you guys are agreeing on. Can
> anyone give a
> > > couple of examples of what this means?
> >
> >MW: examples would be painted, open, approved.
>
> Why would these not simply be properties?
MW: This is just a peculiarity of ours, we have anarrow view of property. We
consider properties to be classes that map to number spaces where greater
than and less than have significance, so things like temperature, weight,
speed, and not open, closed, painted.
>
> > >
> > > >
> > > > >
> > > > > Organisational Level
> > > > >
> > > > > Contains axioms and relations that apply to all classes that
> > > > > define the level of structure, e.g. atom, molecule, cell,
> > > > > organism.
> > > >
> > > >I'm not sure exactly what you mean here. Do you envision
> > > having a predicate
> > > >that would relate a class with a quantitative or qualitative
> > > attribute
> > > >specifying the level of granularity of the class? This
> > > might be a good
> > > >idea, and there is nothing like this in the current version
> > > of the ontology.
> > > >Note that the folks at the Ontology Group at ITBM-CNR have
> > > developed an
> > > >ontology called "Granularity" to cover just this sort of
> > > representational
> > > >need.
> > >
> > > Everyone agrees that there is a need for this, but not many people
> > > know how to do it!
> >
> >MW: I think we have identified some general principles and
> some useful
> >organisational levels(following some of Nicola's work) but I
> agree there is
> >a lot of work to do here.
>
> The key issue is that granularity and inference are fundamentally at
> odds with each other, since if you allow sub-granularity differences
> to be 'invisible', and you allow inferences to be stored and re-used
> (which is valid in almost any semantics), then you can generate
> 'heap' paradoxes (take one grain of sand from a big heap leaves it
> big; taking n away for some n>0 doesn't.) All the proposals I know of
> run into this apparently trivial point somewhere or other.
MW: I think we are at cross-purposes. When I talk about orgaisational level
I mean things like humans are made out of cells, and human and cell are at
different organisational levels. I'm not talking about heaps of sand, and
how many grains make a heap, only that heaps and grains are at different
levels and one is made out of the other.
>
> > >
> ><snip>
> > >
> > > >
> > > > >
> > > > > Set
> > > > >
> > > > > Contains axioms and relations that apply to all mathematically
> > > > > defined sets.
> > >
> > > The idea of a 'mathematically defined' set is a bad idea.
> There is no
> > > clear category of a mathematical definition (as opposed to a
> > > nonmathematical one), and in any case what is in a set isn't
> > > determined by the form of the definition.
> >
> >MW: No but what things are sets is. I only mean here that to
> be a set you
> >must be iteratively constructed,
>
> Oh no no. Consider the set of all noncomputable numbers, for example.
MW: I don't understand. I'm not hot on noncomputable numbers for a start.
>
> >and you can't for example have yourself as
> >a member. As far as I can make out this is common ground for
> what a set is
> >consdered to be. But I'm prepared to hear that the contrary is true.
>
> Actually, there are "non-well-founded" set theories where a set can
> be a member of itself, but they are new and not considered infra-dig
> in many mathematical circles.
MW: So back to shifting sands then I guess :-(
>
> Pat Hayes
>
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>
Regards
Matthew
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