Re: Nonmonotonic rules

pat hayes <phayes@ihmc.us> writes:
>
> >But it seems that the two camps are now on equal footing. Neither has a
> >completely satisfactory solution and both are trying to find one. Why did
> >you say that the non-monotonic camp should "shut up" and "all talk about
> >nonmon systems be ruled out of order"?
> 
> Well, it got the discussion started, right? I admit to having found 
> myself frustrated by the sense that many controversial positions were 
> becoming just accepted as given without adequate discussion, hence my 
> abrupt tone.

It was certainly useful to start the discussion.  One should just be
careful to make no statements that can politicize the field.


> >  >   Being monotonic doesn't mean one has to be
> >>  bone-headed. I would be reasonably happy with
> >>  Theory+Closure+Rn |= false, and having an
> >>  explicit strategy for handling contradictions. We
> >>  need to be able to handle contradictions in any
> >>  case.  One such strategy might be to make an
> >>  explicit assumption that Rn overrides k+1, which
> >>  is thereby treated as a temporary assumption;
> >>  that was the original motivation for
> >>  circumscription, in fact. This gives a globally
> >>  nonmonotonic behavior but keeps explicit track of
> >>  the assumptions in each derivation path, so uses
> >>  monotonic logic *within* a proof. That might be a
> >>  useful compromise, in fact, for practical use.
> >>  Notice that the 'contradiction-handling' is
> >>  explicitly not part of the derivation in this
> >>  case (contrast most treatments of default
> >>  reasoning, for example): the overall reasoning
> >>  pattern is what used to be called
> >>  'truth-maintenance' in AI.
> >
> >Doesn't sound too elegant compared to circumscription, but ok.
> >All that is left is to come up with a reasonable theory.
> >Will be funny if the result will turn out the same as
> >circumscription (for all practical purposes) and will be implemented using
> >the plain old negation as failure (e.g., the well-founded semantics).
> 
> That actually seems quite likely: it is probably best in areas like 
> this to stick to time-tested methods if one can.  But the issue which 
> may be merely terminological to some, but seems crucial to me, is 
> that it is possible to cast circumscription in terms of an 
> *identified* nonmonotonic assumption which can be stated explicitly 
> (the minimization of 'abnormal'), and so this framework allows 
> information to be conveyed within a globally monotonic system of 
> communication.

So, you are saying that you are ok with "compartmentalized" non-monotonicity.
This is what I thought the role of non-monotonicity could be.
I am not ready to rule out other possible scenarios where non-mon can be
used on the SW, but I can't think of any.


> >  > The basic reasoning of the above
> >>  paragraph is from Tim Berners-Lee.
> >
> >
> >He is certainly entitled to his opinion. It may or may not be correct.
> >Unless he has the logical theory that you are still aiming to develop, his
> >"reasoning" is no more than a belief at this point.
> 
> No, this is unfair. The point that Tim made (the words are mine, but 
> the point is his) does not depend on developing a logic. It is a 
> general architectural point about the Web, and can be viewed as a 
> *requirement* on a web logic. If one wanted a more detailed 
> expression of it, the place to look would be the REST architectural 
> theory.

If one understands what he said in a way that doesn't rule out
compartmentalized non-monotonicity, then I think it is reasonable.
But it is hard to tell what he really meant. I think the most plausible
reading was "no non-monotonicity whatsoever". 

In any case, I often find that there is a long way to go from an
architectural picture down to the nuts and bolts, and when the bolts are
supposed to be a logical theory of some sort then that road is usually
thorny and full of surprises.


> >  > >I agree that publishing a statement that makes non-monotonic closure with
> >>  >respect to an unknown set of sources doesn't carry much useful info for the
> >  > >recipient of the statement.
> >>
> >>  That is my basic point, on which we seem to
> >>  agree. The conclusion I draw is that either the
> >>  closure should be with respect to a known, and
> >>  defined, set of sources, or else the statement
> >>  should not rely on a non-monotonic closure.
> >
> >Yes, I agree.
> 
> Excellent. This seems then to be a useful reference point of 
> agreement. I would be happy if this discussion could be conducted on 
> this basis, at least, rather than as being about mon vs. nonmon.

I agree in the sense that I see it as a coherent framework, that I see uses
for this kind of reasoning, and that I don't see uses for something
significantly more general on the SW.

But I am not ready to start going after the heretics yet :-)


> >I specify a schema -- an ontology, if you please.
> >I would say: I take objects of these classes, the classes have these
> >attributes of these types. And the objects must satisfy these integrity
> >constraints. Maybe something else, but this is enough for a start.
> >
> >What I won't say is which sets of objects I am going to close off. You
> >give me those objects and I will reason non-mon with them as long as your
> >objects conform to my schema.
> 
> Ah. That is a completely different view of how the SW operates than I 
> have previously come across, and indeed suggests a resolution of the 
> debate. Let me check my understanding. You see a clean distinction 
> between ontological information and data, and regard talk of classes 
> as belonging to the ontology level: and then a rule may apply 
> (possibly non-monotonically) to a class in the sense that it is 
> applied  to *elements* of this class, ie to data, or objects, which 
> satisfies the class description; and the class itself - or more 
> properly the ontology describing the class - *is* the necessary 
> information about the intended domain of application of the 
> non-monotonic rule. In the terminology I have been using, the entire 
> ontology is 'meta-information' about the applicability of the rule.
> 
> Is that more or less right?


Yes, this is how I was thinking about it.


> This is an elegant way of combining the 
> 'OWL' view of classes, where they are simply the extensions of 
> logical predicates, with the OO (what I think of as the Java) view of 
> classes, where they are categorizations of computational 'objects'.

This is not really a new way of thinking. It is
an overall (idealized) architecture used in the database world. 
You write applications that are supposed to work with any instance of the
database as long as that instance satisfies the schema (i.e., the types
and constraints).

On the SW, the "application" is a bunch of rules and the schema is an ontology.


> >  > >For instance, I can publish a heuristic for planning complex multi-segment
> >>  >trips.
> >>
> >>  OK, but how do you convey the information that
> >>  this is the intended way that your heuristic is
> >>  supposed to be used? You seem (?) to be assuming
> >>  that your publication comes with a kind of
> >>  protective meta-information which lets a reader
> >>  know what the intended purpose, or scope, of the
> >>  rules are.  How is this meta-information supposed
> >>  to be conveyed from the publisher to the reader?
> >
> >I specify the input schema, as above.
> >The exact context is known to you.
> >The type of the context is known to both of us.
> >
> >But this may still not be monotonic, because you give me your sets of facts
> >and I circumscribe them.
> >
> >>  >My heuristic will assume any number of generic inputs and will make
> >>  >decisions based on the available inputs. It will take the inputs provided
> >>  >by the consumer and close them off.
> >>
> 
> I see now that we have been talking at cross purposes. I assumed it 
> would not, because in my understanding of what a nonmonotonic rule 
> would be doing, there was no provision in any of the extant SW 
> standards or protocols for supplying this meta-information. I (think 
> I) see that with your understanding of the role of the rules, things 
> like RDFS and OWL already constitute that meta-information.  However, 
> if I have this more or less right, this view seems to require a more 
> delicate account of the relationship between the rules and the 
> ontology language. The ways that rules relate to class descriptions 
> is rather different here from the way that Ian Horrocks and Benjamin 
> talk about this relationship, where both the rule language and the DL 
> descriptions are simply sublanguages of a common logical framework. 
> For example, there is no notion of 'constraint' in that world, 
> whereas it would seem to be central in your view.

Yes, this is a good observation. In fact, even in OWL alone (forget the
rules) there is no notion completely analogous to constraints in databases.
Many people are confused by the "cardinality constraints" in DLs, but this
is not the same thing. In DLs, cardinality constraints are assertions
about the real world and data never violate those assertions. Instead,
data are "made to fit" the constraints (by adding equality or inventing new
elements).


> >this mailing list is SWS-IG (Semantic Web
> >*Services*). The scenarios that I had in mind come from the domain of
> >agents and service descriptions.
> >
> >SWS \subset SW
> >
> >so when you are saying that something should be ruled out on the SW then I
> >monotonically (!) conclude that this must be ruled out in the domain of SWS,
> >which I don't accept.
> 
> Fair enough, but I think that the resolution of the argument lies not 
> so much in SWS\subset SW as in the *way* that you see SWS using the 
> SW formalisms. I have been assuming that SW content is data: you have 
> been assuming that it is meta-data. If it is meta-data then indeed 
> many of my 'how can that be done??' worries are answered immediately; 
> and in that case, also, my objections to nonmon reasoning do not 
> apply with anything like the same force, or even at all, to 
> data-level reasoning. I need to think about this some more, obviously.


So, vive la (appropriately restricted) non-monotonic SW! :-)


> >But I don't even accept your statement about ruling out non-mon in the
> >context of SW-minus-SWS, because it sounds too sweeping to me -- too
> >non-monotonic :-)
> 
> Point taken. Though I think you really mean, too monotonic :-)

No, non-monotonic. Such a statement includes closed-world negation with
respect to a context that is not really clear :-)

> >My description of the service will say that I am a complex travel planner
> >and I will use simple services, such as Expedia, Orbitz, Avis & Hertz,
> >etc. But you tell me which to use (maybe you know a good service in
> >Thailand, and I might use it for the part of your travel in that part
> >of the world).
> 
> Well, yes, of course I have no quarrel with that: but now, I have a 
> different puzzle: why does this require any *publication* of 
> nonmonotonic rules at all? Why does it require ANY kind of content 
> publication? This sounds to me like a piece of code that is running 
> somewhere and providing a service: it might even be proprietary; in 
> any case, it does not need to be publishable, any more than the code 
> of a query-answering system needs to be publishable.

It probably doesn't need to be published if it is a travel service.
But I can imagine situations where the service is so critical that you
might want to know how it works.

Also, agent-style examples are the easiest to throw around. There are
also much more down-to-earth examples of service-related things that are
convenient to model using defaults. They are just not the neat little things
that one can easily give as examples. I am not even saying that equivalent
modeling cannot be done in a monotonic way. All I am saying is that (as we
already agreed) non-monotonic reasoning patterns can be useful, sometimes
may be indispensable, and they can be made to work in an open environment.

> >But I might be able to prove
> >that whenever it gives a positive answer, the answer is correct with
> >respect to the sources that you gave me. This is all I care in order for
> >the service to make money.
> 
> Fair enough. And that might well be a useful claim to publish, of 
> course, partly in order to help make money.

So, publishing conclusions made non-monotonically can be useful even if
the exact context in which those conclusions were made is not known to the
consumer (only the ontology of that context may be known!).


> >I think we made a lot of progress understanding each other. Our
> >differences are probably not just terminological, but they are
> >smaller than we thought at the outset.
> 
> Indeed. There may be no differences, given my newer understanding of 
> how you intend that nonmon rules are to be used. I think we may have 
> been viewing the world from  different metalevels, as it were.

Suddenly the difference of opinion became fuzzy ...

Unfortunately, nobody had the patience to read this far to find out that we
actually agree :-)


> >But I am fine with your agenda of finding a monotonic framework for the
> >useful patterns of reasoning that are "conventionally understood as non-mon".
> >Good luck to you. (Honest!) But until you find such a framework, I won't
> >accept your sweeping statements about the inapplicability of non-monotonic
> >reasoning on the Semantic Web.
> 
> Terminology again, but I think that I might characterize what you are 
> doing as nonmonotonic reasoning 'under' the Semantic Web rather than 
> 'on' it.

This pun may have some depth to it. You can say that much of what Semantic
Web Services are is "under" the Semantic Web rather than "on" it. I am not
sure that "under" is the only place where non-monotonic reasoning patterns
play a role, but we seem to agree now that they may play a role somewhere
"around" the SW.


	--michael

Received on Wednesday, 21 January 2004 03:18:45 UTC