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Re: LANG: need to CLOSE Issue 5.6 Imports as magic syntax

From: Jeff Heflin <heflin@cse.lehigh.edu>
Date: Tue, 26 Nov 2002 10:36:27 -0500
Message-ID: <3DE394FB.186E64F9@cse.lehigh.edu>
To: pat hayes <phayes@ai.uwf.edu>
CC: www-webont-wg@w3.org

Pat,

The proposal that was approved by the WG is significantly different from
the "A imports B means if B entails P then A entails P" proposal. In
particular the semantics define an imports closure and then says that an
OWL interpretation of a document is defined as the OWL interpretation of
its imports closure. Please see [1] for details. This gives the
semantics in terms of the abstract syntax, but Peter has also added
corresponding information for the RDF compatible semantics (see the
Semantics document). I don't believe your arguments below apply to this
approach to owl:imports, but would like to know if you disagree or
believe there are other problems with the approach.

Jeff

[1] http://lists.w3.org/Archives/Public/www-webont-wg/2002Nov/0004.html

pat hayes wrote:
> 
> >Jim,
> >
> >I believe you are correct that there is consensus on the points you
> >detail below. It seems to me that there are three issues currently
> >unresolved.
> >
> >1) Should an imports failure make the imports statement "true by
> >default" as suggested by Pat in [1]. I argued problems with this in [2]
> >and suggested that the "A imports B means if B entails P then A entails
> >P" solution is better. I have not heard a counter-argument on this
> >point. Perhaps silence can be taken as assent?
> 
> No, you cannot take silence as assent, only that I had other things
> to do for a week or so. (Sorry Ive been behind on webont email. But
> this is a good illustration of the perils of non-monotonic reasoning
> in a distributed environment.) Dan Connolly explained why not some
> time back and I have repeated the point several times, at F2F and in
> emails, but apparently it does not sink in, so I will explain again
> in detail. Basically, the objection is that this 'definition' as it
> stands is either empty or self-contradictory.
> 
> The English word "entails" already has a meaning which is quite
> precise, especially in this kind of context, as follows: A entails B
> means that any interpretation which makes A true also makes B true.
> Or, if you like: B is true in all models of A. To emphasize: that is
> what the English word "entails" MEANS in this context.
> 
> So it just won't do to SAY that "A imports B means if B entails P
> then A entails P" if, in fact, A does NOT entail P. Its like saying
> "A imports B means that if B is green then A is green" when A is red.
> And if, for example, we say that owl:imports has no formal semantics,
> or is 'magic syntax', then the presence of some owl:imports triples
> makes no difference to whether or not A is true in I. So whether or
> not B entails something makes no difference to A entailing it, even
> if A does import B; unless of course that phrase 'A imports B'
> actually means that all of B is literally, syntactically, included in
> A: in which case there is no need to say anything about entailment,
> since in that case it is trivial that A entails anything that B does.
> See http://www.w3.org/TR/2002/WD-rdf-mt-20021112.html,  section 2,
> subgraph lemma. So either way, the proposed definition is dumb. Its
> either false or its vacuous.
>
> To make the point in excruciating detail, consider Jim's example
> where A says (imports B; Joe a man) and B says (man subclass mortal)
> and the question is whether or not A entails Joe a mortal. Well, if
> imports is outside the 'formal semantics', ie has no bearing on the
> truth-conditions, then the answer is unequivocally, no, it does not
> entail it. Because there is an interpretation in which Joe is a man
> but not mortal, and that interpretation makes A true but the
> conclusion false. Of course, it makes B false as well, and A imports
> B. But, by semantic decree, that has got NOTHING TO DO WITH truth in
> interpretations and hence nothing to do with entailment. So the
> suggested 'definition' just does not work if imports doesn't have the
> appropriate truth-conditions in interpretations. 'Magic syntax' isn't
> magic: it's just plain meaningless.
> 
> Now, of course, we can just mis-use terminology to suit our purposes,
> and say that we are re-defining what "entails" means; but if we are
> using some other notion then we really ought to use some other word.
> One option is to say that the use of 'owl:imports' means that we are
> no longer thinking about entailment: the basic semantic relationship
> between documents is not entailment but some other notion, such as
> imports-closure-entailment.
> 
> But there is another way out of the problem. We can specify the
> meaning of owl:imports any way we want, and so impose
> truth-conditions on owl:imports which make "A imports B means if B
> entails P then A entails P" work out true WITH the usual meaning of
> 'entails'. I did that, and sent you an account of the relevant
> truth-conditions which would make your intended meaning of
> owl:imports come out the way you want it to while satisfying the
> usual English meanings of all the words involved. In effect, I took
> your phrase, used the usual meaning of "entails" , and
> reverse-engineered the required truth-conditions. Seems to me that
> this solved the problem. You get owl:imports, it has exactly the
> intuitive meaning and formal consequences that you want it to have,
> "entails" means entails, and the usual advantages of having a precise
> model theory accrue: you can use owl:imports freely in the language,
> take subproperties of it, define classes by restrictions on it, deny
> it, whatever you want.
> 
> But apparently the WG rejected this last week. I confess to being
> totally astonished by this decision. Not wanting to Defend my Work or
> anything, but it solved a problem which is now a problem again. We
> now have owl:imports, and either it doesn't, in fact, mean what we
> say it means, or we aren't talking English. Why in God's name a group
> of intelligent people would decide to use a technical English word
> with an exact meaning, but simultaneously reject the technical
> account which makes the English decision factually correct, is beyond
> me. I am tempted to use modus tollens reasoning to conclude something
> about the WG, but no doubt that would be inappropriate.
> 
> To be fair, those truth-conditions may have been overly complex,
> since if we only allow what I called there 'I-import' assertions then
> we don't need to get into the stuff about tokens and indexicals, and
> the simpler MT trick that Dan C. suggested will work fine. But if we
> are going to talk about imports and entailment in the same breath,
> then we need to have *some* account of the truth-conditions for
> owl:imports. If owl:imports has no effect on truth in interpretations
> then it doesn't have any effect on anything entailing anything:
> that's just a fact.
> 
> >
> >2) Should we have an operational semantics as opposed to a
> >entailment-based smenatics as argued by Massimo [3]. The operational
> >solution is more constraining: it requires developers to implement
> >things in a certain way. The entailment semantics on the other hand
> >allows Massimo to implement his operational solution, but allows other
> >developers to implement things differently. This is a key feature of the
> >entailment-based solution.
> >
> >3) How should error conditions be handled (e.g., 404 errors). Some
> >people have argued that the system should report errors to users, others
> >that additional triples should be added to the graph. I do not think we
> >will reach consensus on this. However, the entailment-based solution
> >once again embraces the various opinions. It simply says if you don't
> >draw all the inferences then your reasoning is incomplete (see [4]).
> >Thus, particular implementors are free to provide warning messages,
> >error messages, meta-information in the graph, or whatever else they
> >choose when such situations arise.
> >
> >Therefore, I propose the following:
> >
> >1) The syntax for imports be the same as that of DAML+OIL
> >
> >2) The semantics essentially be "A imports B means if B entails P then A
> >entails P."
> 
> Saying that it is a 'semantics' means that you need to work out the
> actual truth-conditions on owl:imports to ensure that it really does
> mean this. With the decisions we currently have, this is now not only
> not a semantics, it is plain false. Either that is not what A imports
> B means, or else, if it does mean that, then it's almost always
> false. You can't have it both ways: if its outside the MT, then
> entailment ignores it. If you want it to entail something, then you
> need to make it come out true in the appropriate interpretations. Let
> me emphasize: WITHOUT TRUTH CONDITIONS, THERE IS NO SUCH THIS AS AN
> ENTAILMENT SEMANTICS.
> 
> >Here A and B can be any document, not just ontologies.
> 
> Then we have to say what 'entailment' means when used between
> non-ontology documents, which requires us to say what it means for
> them to be true in an interpretation, which requires us to specify
> what counts as an interpretation of them and the conditions under
> which they are true in it. They start to sound like ontology
> documents to me.
> 
> >  >
> >>  We need to close this issue somehow - suggestions?
> >  >   -JH
> 
> Well, I expect you think you have now closed it, Jim, but I don't
> think in fact you have. All you have done is put a bomb in a
> suitcase. Its going to go off eventually.
> 
> Pat
> --
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Received on Tuesday, 26 November 2002 10:36:46 GMT

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