- From: Jeff Heflin <heflin@cse.lehigh.edu>
- Date: Tue, 26 Nov 2002 10:36:27 -0500
- 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 > -- > --------------------------------------------------------------------- > IHMC (850)434 8903 home > 40 South Alcaniz St. (850)202 4416 office > Pensacola (850)202 4440 fax > FL 32501 (850)291 0667 cell > phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes > s.pam@ai.uwf.edu for spam
Received on Tuesday, 26 November 2002 10:36:46 UTC