# Re: Strawman Model Theory

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 23 Jul 2001 17:49:51 -0700
Message-Id: <v0421010fb7827581df95@[130.107.66.237]>

```>[a correction after some holiday biking]
>
> > > A mapping IEXT : P -> R x R            // R cross R
> >
> > Isn't the notation f: A -> B used for a function with
> > domain A and range B?
> > But IEXT is not a funtion at all, it is a relation on
> > a cross product R x R which is simply a subset of R x R
> > IEXT(I(p)) = {<I(s),I(o)> el R x R: I(s) I(p) I(o) is true}
>
>I was wrong, IEXT is indeed a function but it's range
>seems to be the set of all subsets of R x R
>(including the empty set?)

Right, exactly. The most obvious way to do this would be to have
properties denote relational extensions, ie subsets of RxR. However,
there is a technical advantage to making things just a whisker more
complicated and distinguishing the relation-thing from its extension
(I got this idea from Chris Menzel). Then it is quite kosher to allow
properties of properties, and even properties which apply to
themselves, without getting caught in wierd set-theoretical loops.

I'll explain more fully in a document ready soon (hopefully
tomorrow.) Sorry I have been out of the rdfcore loop for a week and
am trying to catch up.

Yes, the subset of RxR can be empty: that is a property that has no
values (ie is always false).

Pat

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```
Received on Monday, 23 July 2001 20:49:45 UTC

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