# Re: function symbols in SWRL FOL

From: Sandro Hawke <sandro@w3.org>
Date: Thu, 25 Nov 2004 08:24:27 -0500
To: Ian Horrocks <horrocks@cs.man.ac.uk>

Message-Id: <E1CXJbn-0000tV-2y@localhost.localdomain>
```

> Secondly, when we have equality (as we do in SWRL FOL), function symbols
> do not add to the expressive power of the language as we can easily
> substitute "functional" predicates. I was hoping to refer you to a
> suitable logic text book at this point, but one didn't immediately come
> to hand so I will attempt to DIY it. To make a predicate f "functional",
> we simply add:
...

Can we characterize this transform in a few more regards?

1.  The models of the pre-transform formula (F1) and the
post-transform formula (F2) are the same.
2.  It is lossy / not reversable.   You can't look at F2
and figure out what F1 must have been.
3.  For many computational logic systems, the performance
characteristics of operating with F1 will be significantly
different from those of operating with F2.  (Where
"significantly" is perhaps extraneous, because theorem
provers seem to be extremely sensitive to syntactic
transformations.

I've referred to this transform in the past as "deSkolemizing", although
it's not exactly the inverse operation, since neither this transform nor
Skolemizing is reversable.  I think if you keep metadata about the
arbitrary choices made, however, the transformations are inverses.

This is not just of idle interest, since it helps characterize the
relationship of n3's logic with Horn logic.  In n3 we have conjuncts and
local existentials in the consequent, and I believe this transform is
half the demonstration that these features are expressively equivalent
to Horn.

The other half of the puzzle is about the transform between n-ary
predicates and binary predicates (which I wish we could agree to call
dyadic predicates, since the word "binary" has such strong other
associations).   There is a transform which effectively converts n-ary
to 2-ary predicates, but it is not perfectly model-preserving, since it
reifies the relationship.

I expect the relationship of n3 to the SWRL will have to be well
understood before industry consensus can be achieved in this area.

-- sandro
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Received on Thursday, 25 November 2004 13:22:47 GMT

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