Urgent! Semantic question about rdfs:domain.

From: pat hayes (phayes@ai.uwf.edu)
Date: 04/24/01

Checking thru the walk-thru.  The section which introduces properties 
is worded in a way that suggests a different semantics from the one 
given in the model theory.

The example says that the domain of hasParent is #Animal, and this 
clearly suggests that the intention is that this should mean that 
every animal has a parent, ie that hasParent applies to the entire 
domain class (in contrast to the range specification.) I wrote the 
following 'explanation' before realising that it might not be true:

"The range specification restricts the property from 'above', ie it 
specifies a class into which the value of the property must fit, 
while the domain restricts it from 'below', ie it specifies a class 
which must be included in the class of things that the property can 
be applied to. "

Is this correct??  Because if so, the semantics is wrong at this point. It says

<rdfs:domain,?P,?C>    means:    if <x,y> in IR(?P) then x in IC(?C)

but if the above is correct then it ought to say:

<rdfs:domain,?P,?C>    means:   if x in IC(?C) then for some y, <x,y> in IR(?P)

If the semantics is correct, however, then the example in the 
walkthrough is rather misleading, and we will need to correct against 
any potential misunderstanding. Also, in this case, HOW does someone 
give a 'lower' bound to the domain of a property? Eg how can one say 
that hasParent applies to *any* animal? (If both domain and range 
restrict from above, then it would be consistent to give all 
properties empty domains and ranges.)

I await clarification from the Semantic Gurus, and will write 
appropriate prose for the walkthru when clarity is restored to my 

Pat Hayes

PS. A related question. If
does it follow that
    <rdfs:domain, ?S,?R>

PPS. The only way to really learn something is to try teaching it to 
other people :-)

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