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RE: properties as nodes etc.

From: pat hayes <phayes@ai.uwf.edu>
Date: Tue, 9 Jul 2002 11:37:59 -0700
Message-Id: <p05111b2bb950daed5473@[192.168.0.146]>
To: Enrico Franconi <franconi@cs.man.ac.uk>
Cc: www-rdf-logic@w3.org

>On June 27, pat hayes writes:
>>  >[the cat] --[sat on]--> [the mat]
>>  >                 |
>>  >               [for]
>>  >                 |
>>  >                 V
>>  >             [an hour]
>>
>>  Ah, I see where you are coming from. OK, but look, there are several
>>  different things here. There is the property of sitting on
>>  something, in general; there is a particular instance of that
>>  property, which in this case might be something like the cat's way
>>  of sitting on the mat (that's the 'trope'); and then there is a
>>  particular occurrence of a sitting: an event, or happening, or maybe
>>  a 'situation' in Barwise's sense, or what Hobbs calls an
>>  'eventuality'.  Its the latter that have times and places and which
>>  cause other things to happen. I would suggest that if you want to
>>  talk about things like that, then you ought to do so explicitly. One
>>  tried-and-tested idea is to introduce an explicit category of
>>  events, and connect everything else to them.  Then your example
>>  would look like this in Ntriples:
>>
>>  _:x  rdf:type sittingsOn .
>>  _:x  agent cat .
>>  _:x  object mat .
>>  _:x  duration hour .
>>
>>  where you would also know that
>>
>>  sittingsOn rdfs:subClassOf events .
>>
>>  and you could then say other things about that sitting as well, such
>>  as why it happened and what its results were and who told you about
>>  it, and so on. You could even say that it never happened or was
>>  imaginary.
>
>I'm starting with the assumption that the problem here is to represent
>relations with arity greater than two.

OK, that wasn't clear to me at first. In that case, my suggestion 
above may be inappropriate.

>The inability of RDF to express
>such things is one of its (many?) major drawbacks. Note that all
>semantic data models in DB, all conceptual modelling languages in SE
>(like UML), and the most advanced DL do provide such a feature.

RDF is a very simple, basic, inexpressive language. One can point to 
many examples of how it could be 'improved' by increasing its 
expressive powers.

>The above encoding of a ternary relation in a binary relational model
>(like RDF) would be wrong, and in fact it can not be done in RDF at
>all. In fact, you are missing the information that there is a unique
>instance of the ternary relation for each triple of arguments.

Im wasn't "missing" it: I was explicitly not assuming it. The 
rationale for this decision in cases like your example has been 
rehearsed in the linguistics literature. Now, of course, you are 
right that this is not a way to encode the full meaning of a ternary 
relation (as opposed to an eventuality/situation/case which may have 
any number of properties.)

>So, the
>original information stated in the graph making use of the ternary
>relation says that given a cat, a mat, and a specific time, then there
>is a unique instance of the ternary relation (in this case, the event
>of sitting). In your weaker encoding, you may have more than one
>instance of the event for each tuple in the original n-ary
>relation. Clearly, you violate the semantics of n-ary relations, by
>admitting basically that a tuple may appear more than once in the
>relation.

That is not so clear. Clearly a tuple may appear only once in any 
relational extension; but several distinct relations may have the 
same extension. In the example, one might have an ontology which 
admits several possible 'timelines' expressing alternative ways that 
some chain of events might happen (such things are commonplace in 
modal reasoning and AI planning applications, for example.)

>By the way, this is nothing new: in the ER model you do have "weak"
>relations. To encode them you need to add a bunch of functional
>dependencies to guarantee the uniqueness. If RDF had the ability to
>state functional dependencies, then you could do the encoding.

Right, if RDF had a notion of equality it would be considerably more 
expressive.

>Of course, you may decide that you don't have the semantics of a
>ternary relation in the original graph, but then you have to tell me
>which is your model theory for it.

? What I am obliged to do is to tell you the model theory of RDF. RDF 
is a very weak logic which makes no claims to expressive completeness.

>  Possibly a bag semantics could
>solve the problem but -- since you are suggesting the above encoding

I suggested it simply as a possible strategy for expressing your 
intended meaning in RDF. (BTW, even if your objections are correct, 
they show only that the encoding is incomplete, not that it is wrong.)

>-- it is up to you to prove the correctness of the encoding you propose
>wrt this new bag-based MT :-)
>
>Another solution to the problem would be to deny my initial
>assumption: we are not talking about n-ary relations here, and we
>don't want to talk about them ever in RDF. Fine for me.

Well, fine for me also; but I suspect that I do not speak for all 
members of the RDF core WG here :-)

Pat
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Received on Tuesday, 9 July 2002 14:37:48 GMT

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