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Re: ISSUE: DAML+OIL semantics is too weak

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Sun, 19 May 2002 16:58:19 -0400
To: jos.deroo.jd@belgium.agfa.com
Cc: www-webont-wg@w3.org
Message-Id: <20020519165819G.pfps@research.bell-labs.com>
From: "Jos De_Roo" <jos.deroo.jd@belgium.agfa.com>
Subject: Re: ISSUE: DAML+OIL semantics is too weak
Date: Sat, 18 May 2002 14:43:33 +0200

[...]

> From the table
> 
>     Premise     ->     Conclusion
> ----------------------------------------------------
> (1) False     True     False       VALID     UNSOUND
> (2) False     True     True        VALID     UNSOUND
> (3) True      False    False       INVALID   UNSOUND
> (4) True      True     True        VALID     SOUND

I'm still having severe problems in trying to determine what you are
getting at here.  Are you trying to say that a particular derivation is
(in)valid or (un)sound, or that a kind of reasoning is?

> and having that
>   :R a [ owl:complementOf :R ]
> is the same proposition as
>   not(:R a :R)

Well these two should have the same truth value in all interpretations.

> we have the case
>   not(p) -> p
> so only (2) or (3) are to be considered
> but both are UNSOUND

Again, I am totally confused.

> So we aim at (4)'s but in our backing up
> with running cose (just FYI) we don't work
> with the not()'s but instead try to prove
> that the the premise is true and have the
> other rule as candidate but then we are
> no longer on an a so called "Euler path"
> and don't derive from vicious circles.

Are you saying here that your reasoner only uses implications as one-way
rules?  If so, your reasoner is almost certainly going to be incomplete.

> > > I agree that we have to agree on terminology, so how
> > > would you call an argument which is based on assumptions
> > > which are false?
> >
> > Incorrect, or maybe unsound, but I don't see any difference between this
> > kind of argument and an argument that uses an incorrect inference.
> >
> > Maybe you are making a distinction between an argument that uses an
> invalid
> > implication and an argument that uses a non-true premise.  However, there
> > is little difference between the two, as the non-true premise could be
> the
> > invalid implication.
> 
> I agree, that would make no difference.
> It's just that we call such a non-true premise implication
> (and an INVALID implication) an UNSOUND proof argument.

Do you think that this use of ``UNSOUND'' is standard?  If so, please point
me to places in the literature where ``UNSOUND'' is used in this way. 

[...]

> > (It may be that you are trying to say that if ?s has too few known
> ?p-fillers,
> > then there is a contradiction, but this does not follow, nor do many of
> its
> > variants follow.)
> 
> OK, I now see some problems, thanks.
> The point was to count the number of ?p instance pairs
> so I have to make sure to count the proof tree conclusions
> that are different (the cardinality of the proof tree set).
> I think about that infinity...

You appear to be perilously close to
    If I don't know of n differently-named fillers,
    then there can't be n fillers.
which is untrue.

peter
Received on Sunday, 19 May 2002 16:58:34 GMT

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