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Re: Strange behaviour of datatypes test A1 with answer yes and literals untidy

From: pat hayes <phayes@ai.uwf.edu>
Date: Fri, 19 Jul 2002 16:43:27 -0500
Message-Id: <p05111b09b95e2b84e936@[65.217.30.45]>
To: Drew McDermott <drew.mcdermott@yale.edu>
Cc: www-rdf-logic@w3.org

>    [Brian McBride]
>    With reference to Drew's message:
>
> 
>http://lists.w3.org/Archives/Public/www-rdf-comments/2002JulSep/0034.html
>
>    Consider datatypes test A1 with answer YES and literals untidy (i.e. A2 and
>    A3 NO).
>
>    We have:
>
>       <bag1> rdf:_1 "10" .         (1)
>       <bag2> rdf:_1 "10" .         (2)
>    |=
>       <bag1> rdf:_1 _:l .          (3)
>       <bag2> rdf:_1 _:l .          (4)
>
>I don't see why (1) and (2) entail (3) and (4).

Brian has not published the full gory details behind his example. 
Allow me to fill them in, so you can better appreciate the reasoning 
involved here. But be warned, before reading further, that this may 
corrupt your intuitions so badly that your opinions on the test cases 
may become worthless.

OK, if you decide to read on:

We (the WG, that is) found ourselves caught unable to come to a clear 
decision between the two extreme positions of complete tidyness 
(literals are unique, have a fixed denotation) and complete 
untidyiness (literals can mean anything, and different occurrences of 
the same literal can mean different things.) So we have been trying 
to find intermediate positions which capture the best of both worlds. 
One of these positions (we have tried many of them) is the following: 
literals are syntactically tidy (ie like urirefs, there can be only 
one node per literal per graph) but semantically untidy, in that the 
way that the literal is interpreted might depend on the triple in 
which it is considered; in particular, it might be a function of the 
pair consisting of the literal itself and  the property of the 
triple.  This would allow examples like Brian's A example to have the 
same literal 'meaning' two different things in two triples, and it 
allows for 'range datatyping' of properties. Brian however noticed 
that in two cases there seemed to be very much stronger arguments 
against it, in that it seemed to produce inferences which are at best 
highly unintuitive and at worst incoherent. Those two cases involved 
reification and container membership, where the RDF rules themselves 
mandate that certain properties be used (in the above case, the 
rdf:_1  and rdf:_2 membership properties) and hence would impose a 
fixed interpretation of the literal, even when one would wish to 
assume that the 'real' property which determines the literal meaning 
would be some other property (eg in the case of containers, for 
example, it might be the property which has the container itself as 
object in a triple.) Hence examples (and reasoning) like the ones 
given above. Brian's conclusions follow within this 'hybrid' approach 
to literal meanings.

>  We've agreed that
>literals without datatyping information could mean anything at all.

That is the 'extreme untidy' position, which indeed does not support 
so many inferences.

>So how can we conclude that the first "10" denotes the same thing as
>the second "10"?
>
>    We have a cardinality constraint of max 1 on rdf:_1.
>
>    Now add some new triples:
>
>       <bag1> rdf:_1 _:a1 .
>       _:a1   <foo:decimal> "10" .
>
>    This is consistent with (1) above and the cardinality constraint, 
>and also add:
>
>       <bag2>  rdf:_1 _:a2 .
>       _:a2    <foo:binary>  "10" .
>
>    This is consistent with (2) above and the cardinality constraint.
>
>    All together the added statements are consistent with (1) and (2) above,
>    but not with with (3) and (4) above.
>
>Yes, they're inconsistent, which shows that the entailment was incorrect.

Well, sure; but that entailment was indeed valid in the proposed MT 
for literals (which Brian did not elucidate on the broader mailing 
list for fear of letting loose a never-ending debate about 
alternative model theories....oh well.)

Pat
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Received on Friday, 19 July 2002 17:42:53 GMT

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