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problems with concise bounded descriptions

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Thu, 30 Sep 2004 19:39:32 -0400 (EDT)
Message-Id: <20040930.193932.65074452.pfps@research.bell-labs.com>
To: www-rdf-interest@w3.org

In the DAWG message archive I came across a reference to a W3C member
submission from Nokia on Concise Bounded Descriptions

The notion of Concise Bounded Descriptions (CBD) in this note has a number
of problems.

The initial description of a CBD is severely underspecified.  According to
the note, ``A [CBD] of a resource is a body of knowledge about that
resource which does not include any explicit knowledge about any other
resource which can be obtained separately from the same source.''

Problem 1:  Which source?

Problem 2:  What is ``explicit'' knowledge?

Problem 3:  What is ``obtain separately''?

Problem 4:  A function that always returns nothing satisfies this
description, as it certainly does not include any knowledge (explicit or
not) that be obtained (separately or not) from the same source (or indeed
any source at all).

The definition of CBD in terms of a procedure on RDF graphs also has
serious problems.

Problem 5:  Given a node in an RDF graph, there is no general way of
determining which nodes in the graph are co-denotational with that node.
Consider, for example, the RDF graph:
	_:a ex:b _:c .
	_:d ex:e _:f .
What is the CBD of _:a in this graph?

Problem 6:  This definition does not satisfy the initial description of a
CBD.  Consider, for example, the RDF graph:
	ex:a ex:b ex:c .
	ex:r rdf:type rdf:Statement .
	ex:r rdf:subject ex:a .
	ex:r rdf:predicate ex:b .
	ex:r rdf:object ex:c .
the CBD of ex:a in this graph is the graph itself, but it includes explicit
information about ex:r, a potentially different resource.

Problem 7:  This definition does not provide enough information to
distinguish the node from other distinguishable nodes in the graph.
Consider, for example, the RDF graph: 
	ex:r rdf:type owl:InverseFunctionalProperty .
	_:a ex:r _:b .
	_:b ex:r _:a .
	_:a ex:s "NODE A" .
	_:b ex:s "NODE B" .
Then the CBD of _:a in this graph is
	_:x1 ex:r _:x2 .
	_:x2 ex:r _:x1 .
which is the same as the CBD of _:b in this graph but _:a and _:b are
distinguishable in the graph and thus should have different CBDs.

(Definition: Two blank nodes, n1 and n2, are indistinguishable in a graph G
if G with n1 mapped to n2 and n2 mapped to n1 is graph-equal to G (i.e.,
thes sets of triples are exactly the same).  Any node is indistinguishable
from itself.  Two literal nodes are indistinguishable if they mean the same
literal value.  All other pairs of nodes are distinguishable.)

Peter F. Patel-Schneider
Bell Labs Research
Received on Thursday, 30 September 2004 23:33:41 UTC

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