Re: new model theory for DAML+OIL

From: Pat Hayes (
Date: 10/08/01

>From: Pat Hayes <>
>Subject: Re: new model theory for DAML+OIL
>Date: Mon, 8 Oct 2001 10:39:53 -0500
>>  >From: Pat Hayes <>
>>  >Subject: Re: new model theory for DAML+OIL
>>  >Date: Thu, 4 Oct 2001 11:32:29 -0500
>>  >
>>  >[...]
>>  >
>>  >>  >4/ My hope is that the RDF(S) model theory from the RDF Core WG will
>>  >>  >eventually include datatypes.  If this is not the case then I 
>>expect that
>>  >>  >it will be able to admit the DAML+OIL version of datatypes.
>>  >>
>>  >>  I would guess the latter is the likeliest outcome, but its only a
>>  >>  guess. Certainly I would want to at least achieve this as a minimum,
>>  >>  so let us try to keep our work in alignment as far as possible.
>>  >>
>>  >>  It still seems to me that the slight weakening of the
>>  >>  ICEXT(I(rdf:Literal)) condition (to a subset of LV) is all that is
>>  >>  needed to keep the required compatibility, since my LV can be the
>>  >>  union of the ranges of your various literal mappings, and it may
>>  >>  overlap with IR (and if it does, then your two cases for rdfs:range
>>  >>  are both covered by my equation on the intersection.) If you
>>  >>  disagree, can you pinpoint the problem, so I can fix it?
>>  >
>>  >I don't think that this works, because mentioning a literal can make it
>>  >also be a resource.
>>  Inside the RDF WG, the term 'resource' is taken to be synonymous with
>>  'entity' or
>>  'thing'. Everything is a resource, in other words. Apparently you are
>>  using the word in some other sense: can you articulate what your
>>  understanding of 'resource' is?
>I'm equating ``resource'' with IR.  Perhaps this is wrong.  I'll try to use
>IR instead of ``resource'' in future.

OK, fair enough, that was the intent of saying that IR consists of 
resources. But see the proposed change, below.

>  > >Consider
>>  >
>>  >    rdfs:label rdfs:range rdfs:Literal .
>>  >
>>  >    rdfs:range rdfs:label "Range" .
>>  >
>>  >    makes I("Range") in ICEXT(I(rdfs:Literal)
>>  >    so <I("Range"), I(rdfs:Literal)> in IEXT(I(rdf:type))
>>  >    and thus I("Range") in IR
>>  It has to be in IR, yes. And I think that is perfectly reasonable,
>>  since IR is the universe of the interpetation. How about if I just
>>  don't insist that IR consist only of 'resources' (which I took to be
>>  simply a tautology, see above), but say that it is a set of
>>  (resources and literal values)? Would that satisfy you on this point?
>The problem is that you advertise that the model theory was agnostic with
>respect to the relationship between IR and LV.  I took that to mean that
>the model theory would not coerce elements of LV into IR.

OK, but the term 'IR' is an artifact of the model theory, so this 
doesn't really say anything (does it?). The point of the agnosticism 
is to not force literal values to be resources. I personally have no 
problems with saying that they are, since that is on the face of it 
vacuous; but if those in charge of the term 'resource' ever turn 
around and explain that what they *really* mean by 'resource' is in 
fact something quite specific (as I half-suspect, privately, that 
they might one day) I want to be ready with my agnosticism securely 
anchored. I think on balance that the most sensible course for me to 
take would be to just be as noncommittal as possible about the true 
identity of the things in the universe IR, and allow them to be 
literal values (whatever they are) or resources (ditto), and just let 
a uriref denote any damned thing that anyone can possibly think of. 
Would that break your DAML treatment of literals?

Seems to me that we have to allow the semantic possibility of literal 
values being denoted by URIs, even if there is no way to actually 
assert that any particular URI is equal to any particular literal. If 
there was a blanket prohibition on such identity, just using a 
literal name in an RDF graph would produce a global semantic 
constraint, which seems ridiculous.

>  > >However, there is also a more-basic problem with literals.
>  > >
>>  >Literals have a unique mapping into literal values,
>>  I take is as a basic assumption of any denotational language that its
>>  denoting expressions have a unique denotation in any interpretation.
>>  If they don't, the language is too ill-defined to be useable to make
>>  assertions with, as there is no way to know when two tokens are the
>>  same expression or not. So yes, I do make this assumption, and I
>>  insist that we must make this assumption; and if the formalism fails
>>  to keep this true, then the formalism is so broken as to be unusable,
>>  and needs to be fixed.
>I'm not asking that expressions not have a unique denotation in an
>interpretation.  I'm just asking that that the theory of literals not be so

As I understand it, literals *are* expressions. Of a special kind, 
but still expressions.

>>  >which means the
>>  >denotation of both literals below have to be the same.
>>  >
>>  >    <Person rdf:ID="John">
>>  >      <age>05</age>
>>  >      <streetAddress>05</streetAddress>
>>  >    </Person>
>>  That depends on what one counts as being the literal. If the literals
>>  are simply the bare untagged numerals (or numeral strings), then
>>  indeed I would say that we have to say that '5' denotes the same
>>  thing wherever it occurs. But in this case, the obvious way out is to
>>  say that some trace of the tagging is included in the syntactic form
>>  of the literal, so that '5' tagged as an age and '5' tagged as a
>>  streetAddress are *different* literals. That treats the tagging as
>>  part of the syntax, which seems to me to be exactly and precisely
>>  correct, since the tagging is usually referred to as METAdata.
>This requirement is stronger than the previous one, and also stronger than
>the requirements in M&S.

Well, its pretty much required by Tarski, seems to me. We can wriggle 
around it by being very persnickety about exactly what counts as 
'really' being syntax, but isn't it the case that somehow,  something 
has to be able to distinguish the '5' that is an age from the '5' 
that is an address, and that whatever it is that that process is 
accessing could be regarded as part of the 'syntax' of the literal 
for semantic purposes? Seems to me that we could simply adopt this as 
a kind of basic semantic-methodological principle to help us decide 
what counts as part of the 'logical syntax'. We need some help 
keeping all these metadata-ish layers straight in any case.

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