[DL] DL Reasoner

Fernando Naufel do Amaral fnaufel at gmail.com
Wed Feb 9 18:06:08 CET 2011

On Sat, Jan 29, 2011 at 1:48 PM, Cássio Santos <cassio.comp at gmail.com> wrote:
> There are DL reasoners that supports ALCQI+ID?
> Where the ID means that we can represent the unitary cardinality of a
> concept, like a concept can have just one individual.

A few remarks. Please correct me if I'm mistaken.

  1. I have run into the constructor Id(C) as denoting the identity
     relation on a concept C. In other words, it is a role constructor
     such that

        interpr( Id(C) )  =  { (a, a) |  a \in interpr( C ) }

  2. With this meaning, Id(C) can be defined in ALC as

                   \exists Id(C) . D  =  C \dland D

  3. But you say that Id(C) is an assertion to the effect that the
     interpretation of C is a singleton. As Luciano Serafini and
     Markus Krötzsch have pointed out, you can use nominals (in OWL 1
     already) to say that

                               C = {c}

  4. But, to preserve correctness of inferences, nothing else can be
     explicitly asserted about this individual c (which functions
     essentially as a Skolem constant in this context).

     And I think there's a catch here: if you're using the unique name
     assumption, this unique instance c of C cannot be referred to by
     any other name.

     So this definition only works if we drop the unique name

  5. Does the "+" in ALCQI+ID denote the transitive closure operator?
     If it does, it cannot be expressed in OWL 2 DL.



Fernando Náufel, D.Sc.
fnaufel at ic.uff.br

Professor Adjunto
(~Professor Doctor -- see http://en.wikipedia.org/wiki/Professor#Brazil)
LLaRC - Laboratório de Lógica e Representação do Conhecimento
DCT - Depto. de Ciência e Tecnologia
PURO - Pólo Universitário de Rio das Ostras
UFF - Universidade Federal Fluminense

> Thank you in advance,
> --
> Cássio Fernando,
> λSE - Language-oriented Software Engineering research group
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