- From: Francois Bry <bry@ifi.lmu.de>
- Date: Fri, 05 May 2006 11:00:59 +0200
- To: 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.
- 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").
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 09:01:10 UTC