- From: Michael Kifer <kifer@cs.sunysb.edu>
- Date: Fri, 05 May 2006 15:33:23 -0400
- To: Francois Bry <bry@ifi.lmu.de>
- Cc: public-rif-wg@w3.org
>
> Michael Kifer wrote:
> >> Do you really mean this, i.e., that there is essentially only one domain of
> >> discourse? Are there no possibilities of non-trivial identity, for example
> >> between f(a) and f(b)?
> >>
> >
> > With equality the domain of interpretation is a set of equivalence classes
> > over the Herbrand universe. Herbrand universe != Herbrand domain in case
> > there is equality. This is all standard stuff in Logic Programming.
> > http://citeseer.ist.psu.edu/context/6262/0
> > Also see the classical Chang & Lee's book:
> >
> > @book{ chang-lee,
> > author = "C.L. Chang and R.C.T. Lee",
> > title = "Symbolic Logic and Mechanical Theorem Proving",
> > publisher = "Academic Press",
> > year = 1973
> > }
> >
> >
>
> To the beat of my understanding, things can be a little bit more
> differentiated.
>
> There are two approaches to equality in logic programmi9ng and rule
> languages.
>
> - the simple and limited treatment of equality as "syntactical
> equality". In this case, f(a) != f(b) and the (in)equality between
> expressions containing variables is only allowed if these variables are
> bound when this expression is evaluated.
This like "no equality". In standard Prolog the equivalence classes are
each singleton.
>
> - the more complicated one: what Michael has mentioned above. This
> approach is a full treatment of equality at the cost of a significantly
> more complicated reasoning procedure (cf. "paramodulatrion").
Peter was interested in non-trivial equality, I am sure, as in DLs.
--michael
> Many rule languages, especially Prolog and most PR and RR languages,
> have only equality of the first kind.
>
> Francois
>
>
>
Received on Friday, 5 May 2006 19:33:43 UTC