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Yet another approach to literals (take 2)

From: Graham Klyne <GK@NineByNine.org>
Date: Thu, 31 Jan 2002 21:14:43 +0000
Message-Id: <5.1.0.14.2.20020131193400.039df0b0@joy.songbird.com>
To: Jeremy Carroll <jjc@hplb.hpl.hp.com>, Sergey Melnik <melnik@db.stanford.edu>, Dan Connolly <connolly@w3.org>, Pat Hayes <phayes@ai.uwf.edu>, Brian McBride <bwm@hplb.hpl.hp.com>
Cc: www-archive <www-archive@w3.org>
This is a follow-up to my previous response to Pat, in which I run the 
(slightly tidied) revised MT sketch through the various idioms.

(Pat:  I agree that the previous version was too weak, but I don't see that 
it broke self-entailment.)


1. Sketch of model theory (revised)
-------------------------

Starting from RDFS-interpretation per Pat's 30-Jan model theory [1].

1.  We have an interpretation consisting of IR, IEXT, IS, ICEXT.  I propose 
to drop the global mapping LX from literals to LV.

2. A datatype interpretation (DT-interpretation) is specified with respect 
to a specified set of datatypes, DT.  DT is a subset of IC, having an 
additional, externally fixed mapping DTEXT from literals to members of 
ICEXT(DT):
   DTEXT = { <literal,value> | value in ICEXT(DT) }

2a. Define a relation ILOBJ on IPxDT.  Informally, this indicates DT values 
that can be used to "interpret" literal values used in the object position 
of the corresponding property.

3. An interpretation does not assign a specific denotation to 
literals.  Instead, literals are treated like blank nodes with some 
additional constraints.

4. The interpretation of a statement of the form  aaa bbb "foo" .
is defined thus:
    If there exists v in IR and d in DT such that
      <"foo",v> in DTEXT(d) AND ILOBJ(I(bbb),d), AND
      <i(aaa),v> in IEXT(I(bbb)) THEN True, otherwise False.

This basic scaffolding means that an interpretation can arbitrarily 
restrict the members of DT that can be used to interpret a literal object 
of any property.

Also, extend the RDFS-interpretation rules for DT-interpretation so that:

   If ILOBJ(x,y) then <x,y> is in IEXT(I(rdfs:range))

Thus, to be a valid DT-interpretation, the member of DT used to interpret 
object literals for property x must be in the range of x.

This gives us a way of evaluating the truth of a graph that contains 
literals, without actually saying what the literals denote.


2. Apply model theory to idioms
-------------------------------

For the purposes of these examples, I shall assume the existence of three 
members in DT, dtdate, dtusdate, dtukdate and dtstring that correspond to 
date values:

DTEXT(dtdate) = {  :
                   <14-Jul-2001,"2001-07-14">,
                   <15-Jul-2001,"2001-07-15">,
                   <16-Jul-2001,"2001-07-16">,
                    : }

DTEXT(dtusdate) = {  :
                     <07-Jun-2001,"06/07/2001">,
                      :
                     <06-Jul-2001,"07/06/2001">,
                      :
                     <14-Jul-2001,"07/14/2001">,
                     <15-Jul-2001,"07/15/2001">,
                     <16-Jul-2001,"07/16/2001">,
                      : }

DTEXT(dtukdate) = {  :
                     <07-Jun-2001,"07/06/2001">,
                      :
                     <06-Jul-2001,"06/07/2001">,
                      :
                     <14-Jul-2001,"14/07/2001">,
                     <15-Jul-2001,"15/07/2001">,
                     <16-Jul-2001,"16/07/2001">,
                      : }

DTEXT(dtstring) = {  :
                     <"foo","foo">
                      :
                     <"14/07/2001","14/07/2001">,
                     <"14/07/2001","15/07/2001">,
                     <"14/07/2001","16/07/2001">,
                      : }


2.1 Idiom A (per [2]):

   person:Jenny exA:birthDate _:a .
   _:a ex:date "2001-07-15" .

This is satisfied if the node _:a denotes 15-Jul-2001,
and IEXT(I(ex:birthDate)) contains <I(person:Jenny),15-Jul-2001>,
and IEXT(I(ex:date)) contains <15-Jul-2001,"2001-07-15">,
and ILOBJ(i(ex:date),dtstring).

This is consistent with I(ex:date) == dtdate  (described above),
where IEXT(dtdate) == DTEXT(dtdate).

However, other interpretations could be contrived that also satisfy 
this.  An interpretation in which the string "2001-07-15" is an arithmetic 
expression and _:a denotes the number 1979 would also satisfy this graph as 
given.   (Does this really leave us any worse off than we were with untyped 
literals?)

If the range of ex:date is specified to be dtstring [**], the scope for 
creative interpretation is somewhat reduced:  in conjunction with the 
DT-interpretation requirement on ILOBJ this would mean that only dtstring 
can be used to interpret object literals of dt:date.

[**] suggests that a DT-interpretation also needs to indicate a reserved 
vocabulary for the members of DT?


2.2 Idiom B (per [2])

   person:Jenny ex:birthDate "2001-07-15" .
   ex:birthDate rdfs:range ex:date .

This is satisfied if the node "2001-07-15" denotes 15-Jul-2001,
and IEXT(I(ex:birthDate)) contains <I(person:Jenny),15-Jul-2001>,
and ICEXT(I(ex:date)) contains 15-Jul-2001,
and ILOBJ(I(ex:birthDate),I(ex:date))

This is consistent with I(ex:date) == dtdate.  The range specification on 
ex:birthDate prevents any other member of DT being used to interpret the 
literal unless it also maps the string "2001-07-15" to a value related to 
I(person:Jenny) by I(ex:bithDate).


2.3 Idiom D (per [2]) (also P per [3])

   person:Jenny ex:birthDate _:d .
   _:d rdf:value "2001-07-15" .
   _:d rdf:type ex:Date .

This is satisfied if the node _:d denotes 15-Jul-2001,
and IEXT(I(ex:birthDate)) contains <I(person:Jenny),15-Jul-2001>,
and the node "2001-07-15" denotes 15-Jul-2001,
and IEXT(I(rdf:value)) contains <15-Jul-2001,15-Jul-2001>
and ICEXT(I(ex:date)) contains 15-Jul-2001.

This is consistent with I(ex:date) == dtdate,
and IEXT(I(rdf:value)) = <v,v> forall v in IR ?

However, in this case I can see no way to disambiguate, say:
   _:d rdf:value "06/07/2001" .
and
   _:d rdf:value "07/06/2001" .
because (assuming rdf:value is a generic property) there is no obvious way 
to make the graph restrict the datatype used to interpret the literals.



2.4 Idiom E (per [2])

   person:Jenny ex:birthDate _:e .
   _:d rdf:type ex:Date .
   _:d ex:ISO8601 "2001-07-15" .

This is satisfied if the node _:e denotes 15-Jul-2001,
and IEXT(I(ex:birthDate)) contains <I(person:Jenny),15-Jul-2001>,
and ICEXT(I(ex:date)) contains 15-Jul-2001,
and the node "2001-07-15" denotes 15-Jul-2001,
and IEXT(I(ex:ISO8601)) contains <15-Jul-2001,15-Jul-2001>,
and ILOBJ(I(ex:ISO8601),dtdate))

This is consistent with I(exE:date) == dtdate, and the range constraint on 
ex:ISO8601 restricts

On the surface, this is no different from idiom D, but a range constraint 
on the definition of ex:ISO8601 could be used to restrict the satisfying 
literals.  Suppose the range is dtISO8601, a member of DT.  The value space 
of dtISO8601 would be the same as that of dtdate, but the mapping may be 
more restricted;  DTEXT(dtIS8601) a subset of DTEXT(dtdate); e.g.

DTEXT(dtdate) might contain
    { <15-Jul-2001,"15/07/2001">
      <15-Jul-2001,"07/15/2001">
      <15-Jul-2001,"2001-07-15">
      <15-Jul-2001,"20010715">
       : }

but DTEXT(dtISO8601) might contain just
    { <15-Jul-2001,"2001-07-15">
      <15-Jul-2001,"20010715">
       : }


2.5 Conclusion from fitting idioms

All of the above idioms are consistent with a single interpretation of 
ex:birthDate and ex:Date (the main argument against proposal S):

IEXT(I(ex:birthDate)) contains <I(person:Jenny),15-Jul-2001>, i.e. relates 
Jenny to the date value in ICEXT(dtdate) that is her birth date, and

I(ex:date) == dtdate

In response to Pat's comments, I've tried to think about the extent to 
which nonsensical interpretations can be made to satisfy the graphs -- it 
seems to me that being able to use a rdfs:range top restrict the applicable 
literal mappings leaves us at least as well of as we were under any of the 
other proposals.


3. Entailments
--------------

I think it's intuitively clear from section 1 that any graph entails 
itself, without depending on literals being tidy.  There's no way to say 
that a literal means one thing in one instance of a graph, and something 
different in another instance.

Roughly, a literal means any "conforming" value in any graph in which it 
appears, where "conforming" is defined in terms of the set DT with respect 
to which an interpretation is defined, which does not change between 
instances of a graph under the same interpretation.

[I'm not sure I know how to prove this formally.]


4. Other issues
---------------

Values without literal representations.  One of my (lesser) objections to 
DTL was that it didn't account well for values with no literal 
representation.  By having literals denote values, not pairs, I think that 
objection disappears.

This whole approach leaves open the matter of query semantics, other than 
allowing that (adapted from [4]):

     _:f <dc:Title> "10" .
     <mary> <age> "10" .

entails:

     _:x <dc:Title> _:y .
     _:z <age> _:y .

in the absence of further type constraints, and assuming that there exists 
a member of DT which relates "10" to some value.  What is less clear is 
what answers one might such a query to actually return, because there is no 
defined denotation for the literals.  One (reasonable) answer would be to 
simply return the literal (string) and say nothing about its denotation:  I 
think that would correspond to the query semantics that Dan is assuming.  I 
think other answers are possible and reasonable (and out of scope for this 
group).

Backward compatibility with "untyped" RDF.  If the set DT always includes a 
type (say) dtstring (described above), where (say) DTEXT(I(rdfs:Literal)) 
== dtstring, I think this provides a basis for the kinds of string-based 
entailment that Dan expects.  In the absence of any specific typing 
information, a literal can always be interpreted as itself.


5. References
-------------

[1] Pat Hayes, RDF Model Theory, Jan-2002
http://www.coginst.uwf.edu/users/phayes/w3-rdf-mt-current-draft.html

[2] Graham Klyne, RDF Datatyping Desiderata, 25-Jan-2002
http://lists.w3.org/Archives/Public/www-archive/2002Jan/0139.html

[3] Sergey Melnik, RDF Datatyping, 18-Jan-2002
http://www-db.stanford.edu/~melnik/rdf/datatyping-20020118/

[4] Dan Connolly, note on datatyping and query-as-entailment, 30-Jan-2002
http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2002Jan/0440.html




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       /\ \    Graham Klyne
      /  \ \   (GK@ACM.ORG)
     / /\ \ \
    / / /\ \ \
   / / /__\_\ \
  / / /________\
  \/___________/
Received on Thursday, 31 January 2002 17:26:05 GMT

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