Re: Issue-31: Disjoint sorts - sketch of test case

Thanks for the examples, Dave.

One source of confusion about the four levels here seemed to come from 
my use of "semantic objects" in [1].  I'm not sure of a better way to 
express it, but one of the more obvious ways the difference between 
ONDS and OS manifests is if there is equality in the language (as Dave 
shows).

In ONDS, you need seperate operators for stating identity between 
individuals and between predicates, etc, e.g.:

(eq-ind P Q) means that the individuals P & Q are identical.

(eq-pred P Q) means that the predicates P & Q are identical.

Many ONDS systems don't support equality for predicates, so that (as 
in Dave's examples and mine below) = is used for individuals only. 
Also in ONDS it is impossible to say the the predicate P is equal to 
the individual Q (This is because in the semantics the predicate P and 
the individual P are not the same ...err... object? entity? thing?) In 
OS the "predicate P" and the "individual P" are the same thing.

So if you have

P(Z)
Q(P)
R(Q)
P=Q

Just by substitutivity of identicals, in ONDS |-
Q(Q)
R(P)

In OS |-
Q(Q)
R(P)
Q(Z)
P(P)

I hope this makes it clearer, if so I'll add it to the wiki page.

-Chris


[1] http://www.w3.org/2005/rules/wg/wiki/Issue-31


-- 
Dr. Christopher A. Welty                    IBM Watson Research Center
+1.914.784.7055                             19 Skyline Dr.
cawelty@gmail.com                           Hawthorne, NY 10532
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Received on Thursday, 19 April 2007 00:11:51 UTC