Re: new model theory for DAML+OIL

From: Pat Hayes (
Date: 10/04/01

>Here is a new version of the model theory for DAML+OIL that I have been
>working on for the past few days.
>A few points with respect to the model theory.
>1/ Although there are differences between this model theory and the model
>theory for RDF(S) that Pat Hayes has produced, the only significant
>difference from what I believe will be the next version of Pat's model
>theory is the treatment of literals.  Unfortunately, this is a rather major
>2/ I have modified my model theory for DAML+OIL to work somewhat better
>with respect to DAML+OIL datatypes.  This has made it look somewhat
>different from Pat's model theory for RDF(S).
>3/ To support the DAML+OIL version of datatypes (actually a slight
>modification of the DAML+OIL version of datatypes that does not incorporate
>the rdf:value mechanism) I have created my own version of the new model
>theory for RDF(S).  
>I have included my RDF(S) model theory in this message as a separate
>attachment.  Note that my RDF(S) model theory incorporates DAML+OIL
>Note also that my RDF(S) model theory is a text file.  This is supposed to
>reflect its unofficial and draft status!!!  Please don't consider it as
>anything but a temporary support for the DAML+OIL model theory.
>4/ My hope is that the RDF(S) model theory from the RDF Core WG will
>eventually include datatypes.  If this is not the case then I expect that
>it will be able to admit the DAML+OIL version of datatypes.

I would guess the latter is the likeliest outcome, but its only a 
guess. Certainly I would want to at least achieve this as a minimum, 
so let us try to keep our work in alignment as far as possible.

It still seems to me that the slight weakening of the 
ICEXT(I(rdf:Literal)) condition (to a subset of LV) is all that is 
needed to keep the required compatibility, since my LV can be the 
union of the ranges of your various literal mappings, and it may 
overlap with IR (and if it does, then your two cases for rdfs:range 
are both covered by my equation on the intersection.) If you 
disagree, can you pinpoint the problem, so I can fix it?

>If the former
>happens, then I will abandon my RDF(S) model theory.  If the latter
>happens, then I will probably take the datatype model theory from my RDF(S)
>model theory and create an RDF and/or RDFS model theory with datatypes as
>an extension to the RDF(S) model theory.  I will then build the DAML+OIL
>model theory on top of that extension.
>5/ I hope that other description logic theoreticians will be motivated to
>see if this new model theory has any untoward implications.

Right, I would be very interested in this also. The chief issue, I 
think, is that the use of explicit extension mappings in this style 
of model theory allows the syntax to be highly reflexive, in that 
classes can contain themselves, relations apply to themselves, and so 
on, quite freely. In general, membership and application can be used 
freely in ways that would seem to violate the axiom of foundation. 
(Chris Menzel calls this 'wild west syntax'.) I wouldn't expect that 
this would produce any real computational problems in inference, 
other than needing to be aware of the possibility of things like 
class-membership loops (which however have no implications of 
identity, unlike subclass loops) , since the usual logical inference 
machinery works for the wild west syntax almost without change; all 
one has to do is to allow unifiers to treat the function/relation 
position in logical expressions in exactly the way they currently 
treat terms in all the other argument positions.


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