Re: Joint Committee telecon today 11 December

From: Ian Horrocks (
Date: 12/11/01


Regarding the UML encoding. The reason for needing qualified number
restrictions is that the encoding reifies relations so that nary
relations can be dealt with. Roughly speaking, cardinality constraints
on the participation of classes in relationships thus end up as
qualified number restrictions where the property is the inverse of the
property used to link reified relationship to the class and the
qualifier is the reified relationship class. 

Note that because of the encoding is quite complex, it doesn't result
in a useful KB - it can better be seen as a trick for using a DAML+OIL
reasoner to decide problems in an nary DL (called DLR) that can be
used to capture the semantics of data modelling formalisms such as EER
and UML.

Full details from the usual source (Calvanese and Lenzerini). E.g.:

D.~Berardi, D.~Calvanese, and G.~De~Giacomo.
\newblock Reasoning on {UML} {C}lass {D}iagrams using {D}escription {L}ogic
  {B}ased {S}ystems.
\newblock In {\em Proc. of the KI'2001 Workshop on Applications of Description

D.~Calvanese, M.~Lenzerini, and D.~Nardi.
\newblock Description logics for conceptual data modeling.
\newblock In {\em Logics for Databases
  and Information Systems}, pages 229--263. Kluwer Academic Publisher, 1998.

You can probably download these from Diego's web site:

Regards, Ian

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