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Re: need to determine what RDF is

From: Graham Klyne <GK@ninebynine.org>
Date: Fri, 31 May 2002 11:24:09 +0100
Message-Id: <5.1.0.14.2.20020531105500.03e00210@joy.songbird.com>
To: patrick hayes <phayes@ai.uwf.edu>
Cc: <www-rdf-comments@w3.org>

At 02:42 PM 5/30/02 -0500, patrick hayes wrote:
>>>  Yes, but my point is that this logical interpretation is *not* RDF
>>>  entailment.  It is, instead, RDFS entailment.
>>
>>I still fail to see why it is important for us to classify entailments.
>>It's just going to over complicate stuff needlessly.  If my agent knows the
>>rules for rdfs:subClass, than it can arrive at legitimate entailments,
>
>There is no universal overriding notion of 'legitimate' entailment, is 
>why. I agree it complicates things, but I see no way around the fact that 
>life is complicated.

I agree - there can be no universal entailment, except in the trivial sense 
outlined below.

Further, this discussion makes me think that classification of entailment 
types is precisely something that should be considered.

I can imagine a class (not rdf:Class) of rdf:Properties whose intended 
interpretation is to relate N3-formulae resources according to different 
entailments;  e.g., using N3:

{ ant-graph } ent:no-entailment { con-graph } .
-- is always false

{ ex:x rdf:type ex:foo } ent:rdf-entails { [rdf:type ex:foo] } .
-- is true

{ <ex:Jane> <rdf:type> <ex:Woman> .
   <ex:Woman> <rdfs:subClassOf> <ex:Human> }
ent:rdfs-entails
{ <ex:Jane> <rdf:type> <ex:Human>. }
-- is true, but

{ <ex:Jane> <rdf:type> <ex:Woman> .
   <ex:Woman> <rdfs:subClassOf> <ex:Human> }
ent:rdf-entails
{ <ex:Jane> <rdf:type> <ex:Human>. }
-- is false

{ ant-graph } ent:foo-axiom-entailment { con-graph } .
-- is true if some specification or authority 'foo' axiomatically asserts 
the entailment.

{ ant-graph } ent:universal-entailment { con-graph } .
-- is always true

Under the rdfs:subProperty relation, treated as a partial ordering, these 
entailments would form a lattice with ent:universal-entailment as 'top' and 
no-entailment as 'bottom'.

Further, I think one would wish to require that ent:rdf-entailment is a 
subproperty of all other entailment properties.  Maybe also 
ent:rdfs-entailment (other than of ent:rdf-entailment), so we end up with a 
lattice something like this:

         ent:universal-entailment
              |
         .   .   .   .

[ various other flavours of entailment ]

         .   .   .   .

         ent:rdfs-entailment
              |
         ent:rdf-entailment
              |
         ent:no-entailment

Of course these are all just intended meanings -- there's no way to 
logically deduce them using just RDF/RDFS or even full FOL.  But what this 
does is suggest a vocabulary that allows agents to indicate *how* they 
arrive at certain conclusions, and acceptance of such conclusions can be 
tempered by whether other agents agree that the method used is valid for 
their purpose.

I think this makes the limited scope of RDF-entailment (and 
RDFS-entailment) quite explicit, provides a hook for linking RDF inference 
to the anticipated web-of-trust developments, and also provides an explicit 
marker for noting inferences that are the result of some logical reasoning 
as opposed to those which result from some non-logical (and sometimes 
illogical) reasoning including things like "because it's the law".  Thus:

{ :I ex:owe [ ex:to :U ; ex:amount "1" ; ex:denomination UScur:dollar ] }
ent:US-money-entails
{ :I ex:owe [ ex:to :U ; ex:amount "4" ; ex:denomination UScur:quarter ] }

#g


-------------------
Graham Klyne
<GK@NineByNine.org>
Received on Friday, 31 May 2002 07:15:56 GMT

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