Re: equivalentTo / sameClassAs / sameIndividualAs puzzle

From: pat hayes (phayes@ai.uwf.edu)
Date: 07/13/01


>On July 12, pat hayes writes:
> > >On July 9, pat hayes writes:
> > > > >On Mon, 9 Jul 2001, Jeff Heflin wrote:
> > > > >
> > > > > > Ian Horrocks wrote:
> > > > > > >
> > > > > > > On July 7, Dan Brickley writes:
> > > > > > > >
> > > > > > > > I was concerned mostly with the classes case as I'm
> > >thinking about the
> > > > > > > > subClassOf cycles issue. Reading on, same goes for 
>samePropertyAs,
> > > > > > > > sameIndividualAs; it seems equivalentTo is the odd one
> > >out, by talking
> > > > > > > > about 'terms'.
> > > > > > >
> > > > > > > You are reading more into the use of "terms" than was 
>intended. It is
> > > > > > > just an attempt to be vague/general w.r.t. the kinds of
> > >thing that are
> > > > > > > being stated to be equivalent.
> > > > > > >
> > > > > >
> > > > > > I think the definition for equivalentTo should say that "X is an
> > > > > > equivalent resource to Y," where resource is as defined 
>in RDF. Since
> > > > > > RDF resources can be classes, properties or anything else 
>given a URI,
> > > > > > this is compatible with the various subproperties of equivalentTo.
> > > > > > sameIndividualAs is different from equivalentTo because 
>the set of DAML
> > > > > > individuals do not include classes or properties.
> > > > >
> > > > >Aha! That's it. From reading the spec, it wasn't entirely clear to me
> > > > >what DAML+OIL terms individuals. The schema definition suggests its a
> > > > >synonym for 'thing':
> > > > >
> > > > >	<Property rdf:ID="sameIndividualAs">
> > > > >	<rdfs:label>sameIndividualAs</rdfs:label>
> > > > >	<rdfs:comment>
> > > > >	for sameIndividualAs(a, b), read a is the same individual as b.
> > > > >	  </rdfs:comment>
> > > > >	<rdfs:subPropertyOf rdf:resource="#equivalentTo"/>
> > > > >	<rdfs:domain rdf:resource="#Thing"/>
> > > > >	<rdfs:range rdf:resource="#Thing"/>
> > > > >	</Property>
> > > > >
> > > > >Could someone explain to me which things precisely are considered
> > > > >individuals? I gather properties and classes are out of the
> > > > >picture. Any others?
> > > >
> > > > My understanding is that 'individual' is synonymous with 'DAML+OIL
> > > > object' and simply means anything in the semantic domain. The use of
> > > > 'individual' for anything in the domain of quantification is a
> > > > familiar convention in logic, but maybe it needs to be spelled out
> > > > for a wider audience.
> > >
> > >I don't believe this is quite correct. As far as I am concerned, the
> > >denotation of an individual is an object in the domain of discourse,
> > >and there is nothing to prevent two individuals from denoting the same
> > >object (this is what sameIndividualAs asserts).
> >
> > So you are using 'individual' to refer to a *syntactic* entity, ie a
> > name of some kind? That is a very unusual usage, but we can go that
> > way if people want to. However we then probably should rename
> > 'sameIndividualAs' to 'sameObjectAs', since there would be little
> > point in asserting it only of the same name used twice.
>
>I think we are just mis-communicating here, and it is probably my
>fault! I take e.g. "person" to be the name of a class; its denotation
>is a set of elements in the domain of discourse. When I say
>(sameClassAs person human) I am asserting that person and human denote
>the same set.

I presume you mean that "person" and "human" denote the same set? (As 
it stands, you seem to be saying that "person" denotes something that 
denotes a set, but I have no idea what that something could be (it 
isn't the set, presumably, and it isn't the six-character name 
"person", but a third thing that stands between them?) So I will 
guess that this interpretation is wrong.)

> I take e.g. "ian" to be the name of an individual; its
>denotation is a single element in the domain of discourse.

Right, that is my own usage also, with correction noted. But then you say:

>When I say
>(sameIndividualAs ian ihorrocks) I am asserting that ian and ihorrocks
>denote the same element. These two usages seem pretty consistent.

Not to me. If you had said that saying (sameIndividualAs ian 
ihorrocks) asserts that "ian" and "ihorrocks" denote the same 
element, then that would have been consistent. As it stands, however, 
you *seem* to be saying that ian - which I took to be a person, not a 
name - denotes something. Its up to you, of course, but personally, 
myself, I try not to denote unless it is absolutely necessary.

>We could quite reasonably call the element in the domain of discourse
>that is denoted by ian

Do you mean , denoted by "ian" ? If you are doing the denoting, 
rather than being denoted by the name "ian",  then I really have no 
way to know what it is that you denote.

>an individual.

Well, I would say that the element in the domain of discourse is 
indeed an individual. That is what the term 'individual' usually 
means, right?

>This can get a bit confusing,
>however, (as in this case) because I/we are often a bit lazy and refer
>to "ian" as an individual

Really? So you really do mean 'individual' to refer to a syntactic 
category; to words rather than to things? That is not a usage I have 
come across before, and I think it is likely to produce a lot of 
confusion. Why don't we use a term like 'individual variable' or 
'individual name' for the syntactic entity (the denoter) and 
'individual object' (as opposed to 'class object', eg.) for the 
individual thing denoted? This is a bit longwinded but has the merit 
of being very unambiguous.

> rather than the name of an individual (and
>to person as a class rather than the name of a class)

Well yes, person is a class. "person" is the name of the class.

Pat

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