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Re: Concrete and abstract domains disjointness

From: Pat Hayes <phayes@ihmc.us>
Date: Mon, 10 May 2004 10:56:32 -0500
Message-Id: <p06001f40bcc551197691@[10.0.100.76]>
To: "Dimitrios A. Koutsomitropoulos" <kotsomit@hpclab.ceid.upatras.gr>
Cc: www-rdf-logic@w3.org

>Hello,
>
>Can somebody explain some formal reason why the concrete and abstract
>domains (i.e. the datatype and individual sets) have to be disjoint in OWL
>DL?

The rationale that was offered at the time was basically that 
datatypes can introduce arbitrarily complex conditions on class 
definitions, so that to allow datatyped values into a non-datatype 
class means that a (complete) reasoner might have to incorporate 
arbitrarily complex reasoning about domains defined by external means 
and this would infect the entire DL reasoning, with potentially 
disastrous effects on efficiency and even decideability. For example, 
allowing xsd:integer values into normal classes in effect adds 
arithmetic to the DL, since these values are required by the semantic 
conditions to be real, honest-to-God integers, and it is then 
possible to set up restrictions so that to determine class membership 
might require arbitrarily complex arithmetic calculations, eg the 
identity of two individuals might depend on whether a complex 
diophantine equation has one or two solutions. For a more prosaic 
example, the RDF built-in datatype rdf:XMLLiteral would require that 
every reasoner be able to deal with class reasoning over the domain 
of normalized XML documents, so that identity might depend on whether 
or not two XML documents normalized appropriately, eg  if {a, b, 
XMLdoc1, XMLdoc2} has cardinality 3.

By restricting datatypes to datatype classes, the problem is kept 
within manageable bounds and can often be farmed out to external 
reasoners specialized for each datatype, since datatype reasoning can 
be largely kept separate from reasoning about individuals.

>Is there a description logic that drops this restriction?

I do not know, but others might.

I think that this is not really so much a DL-specific restriction as 
one which was imposed on what might be called general 
reasoner-engineering grounds. That is, one could make out a case for 
this style of restriction independently of the logical nature of the 
non-datatype part of the system. The SWRL proposal for example treats 
datatyping as a matter to be handled by 'built-ins', ie function 
calls to external evaluators, which is a similarly motivated 
separation of datatype value handling from (in this case) rule 
processing.

Pat Hayes

>
>
>Many thanks,
>
>Dimitrios A. Koutsomitropoulos
>
>Computer & Informatics Engineer
>Postgraduate Researcher
>High Performance Information Systems Laboratory
>
>  Contact
>  e-mail: kotsomit@hpclab.ceid.upatras.gr
>  work:  +30 2610 993805
>  fax:    +30 2610 997706
>  http://www.hpclab.ceid.upatras.gr


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Received on Monday, 10 May 2004 11:56:34 UTC

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