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Re: Impact of monotonicity in RDF (was: Social Meaning and RDF)

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 10 Feb 2003 12:41:25 -0600
Message-Id: <p05111b27ba6d9b239503@[]>
To: Seth Russell <seth@robustai.net>
Cc: www-rdf-interest@w3.org, Graham Klyne <GK@ninebynine.org>

>pat hayes wrote:
>>>Graham Klyne wrote:
>>>>Above, I've tried to answer your question "could you elaborate on 
>>>>what this restraint really entails" (or maybe what it does not 
>>>>entail?).  One has to choose the meaning of one's terms with a 
>>>>little care.
>>>>You also ask how this is "useful";  my explanation above suggests 
>>>>the reverse -- monotonicity is in some respects an impediment. 
>>>>But in an open-world environment, in which one can *never* be 
>>>>sure of having all of the facts to hand, no conclusions can be 
>>>>drawn without an assumption of monotonicity.  So if we are to 
>>>>make inferences in such circumstances, we must have a monotonic 
>>>Im sorry but I cannot grok this reasoning. Granted, we cannot 
>>>assume we have all the facts.
>>>Granted, the truth of our conclusions are always dependant upon 
>>>the truth and *completness* of our premises.
>>Wrong. The truth of the conclusions does not depend on the 
>>completeness of the premises. That is exactly the point. If it did, 
>>it would be impossible to draw any conclusions, because you cannot 
>>know your premises are complete (unless of course one of them 
>>actually asserts this somehow.)
>Well, ok, that is exactly the point of monotonic logic.  Common 
>sense, however, tells us that for every rule there is an exception. 
>The more exceptions we have discovered, the more confidence we can 
>have in our conclusions.  Evidently the logic your guys have chosen 
>for the semantic web goes against that common sense.  The question 
>is:  why you  think that is a good idea. ?

It seems like a good idea to use the same logical framework that 
almost all existing KR software is one way or another based on and 
which has been a reliable foundation for mathematical and practical 
reasoning in a large variety of domains for over half a century. We 
didnt choose a logic off the shelf, as a casual choice among a 
variety of options. The  overall design is more or less forced upon 
us by circumstances. If you think we could have done it differently, 
please suggest some details. Its no good just appealing to 'common 
sense'; if we know anything about software agents, it is that they 
don't have common sense. However, we can build them to conform to 
standard logical principles, which will  be better than having no 
principles at all to build them on. In fact, speaking now for myself 
personally, I would prefer to think that my software agents were 
applying logical principles perhaps a little too cautiously and a 
little too rigorously, rather than the alternative scenario in which 
they were using their sadly limited abilities at common sense to jump 
to God knows what unintended conclusions. I'd rather ask my cat to 
drive an SUV.

>>>  How can monotonicity change that predicament in the slightest?  I 
>>>keep hearing:  "We know that we cannot conclude such-and-such 
>>>because we might be missing some information, so we *must* change 
>>>all the vocabulary and inference patterns to  be monotonic,  and 
>>>then  we *can* draw such a conclusion.   Huh, what changed - what 
>>>suddenly made drawing unwarrented conclusions valid?   How can we 
>>>suddely make statements that are always true?
>>Its easy to make statements that are always true. One sure way is 
>>to make them linked to a particular time, and include the time in 
>>the assertion. Then if they are ever true, they are always true. 
>>Almost all temporal databases are full of stuff that is always true.
>Unfortunately in RDF we cannot time stamp our triples.  Can we?

No standard mechanism is provided, but many people feel that this 
would be an obvious and desirable next step, and there are working 
groups looking at the details (which are quite intricate, eg 
achieving interoperability between different calendar systems). And 
you are free to think of, and use, one yourself: if it is generally 
useful, maybe others will use it also. The more the merrier, we need 
all the good ideas we can find here.

>>>>Having an monotonic, open-world framework does not, in my view, 
>>>>mean that one cannot also have a locally applied closed-world 
>>>>assumption for some applications, but this strays outside the 
>>>>globally specified behaviour for RDF.  And the conclusions drawn 
>>>>by such an application cannot be returned to the global semantic 
>>>>web (unless somehow qualified by some expression of the closed 
>>>>world assumption used -- which might be presented as a "context").
>>>But we have no way to present a "context"  with RDF  statements. 
>>>Everything in RDF seems always to be true regardless of its 
>>Right. That is admittedly a simplification of the real world 
>>situation, but its not fatal, since we can always encode the 
>>context in the assertion and thereby render it non-contextual (or 
>>at any rate non-contextual enough to be useful.)
>Again RDF does not provide a standard mechinism to do this.  This 
>may be an argument in favor of monotonic logic but not monotonic 
>logic + RDF;  unless you can show us how we *can* encode the context 
>in our RDF assertions in a practical manner.   Can you?

I can think of several ad-hoc ways to do it, but I don't think that 
there is any point in doing this at present as this is more a 
theoretical problem than a practical one, in my experience so far. 
I'm sure it will happen fairly soon, probably in RDF-2.

>>>Of course we all know that's absurb.  I really dont see how 
>>>monotonic logic helps us here - rather the other way around.  It 
>>>seems to lead people to believe that all of their RDF conclusions 
>>>will always be valid and that discovering new information cannot 
>>>change those conclusions.
>>The issue is rather more limited than this. When specifying the RDF 
>>standard, we need to give the thing a semantics which makes this 
>>universal assumption. If we do not, then ALL RDF inferences will be 
>>risky and unsound: any inference you make, anywhere, could be 
>>refuted by something you learn later. If we did this, almost the 
>>entire Web traffic would be taken up with "whoops, sorry, I was 
>>wrong about that"  messages.  All the spec does, in fact, is say 
>>that IF you use RDF content in a nonmonotonic way - for example if 
>>you assume that you have all the relevant information about 
>>something and assume that anything missing is false - then you are 
>>on your own. YOU have made this assumption, taken this risk. But of 
>>course you are free to do so: its just that the spec says, RDF no 
>>longer guarantees that your conclusions follow from your inputs, 
>>OK? The guarantee only applies to monotonic uses. Its like reading 
>>on the box: "Warning: if used indoors may cause risk of fire". It 
>>doesn't mean, don't use indoors. It just says: if you do use it 
>>indoors and it catches fire, don't come blaming us.  If you use RDF 
>>nonmonotonically and you get false conclusions from true premises, 
>>don't come blaming the RDF spec. We warned you on the box.
>Well I have found that in general inferences *are* risky and that 
>they *are* frequently refuted by something that I later learn.

Well, then by all means suggest how we might use this notion of 
inference in an SW standard. Its not enough to just say: entailments 
can be freely rescinded later, when they are no longer felt to be 
useful. We need a coherent global set of conventions for defining how 
to design software which can handle such changes of mind. I don't 
think you will find it easy to do.

And in any case, I would take issue with your claim. I suspect that 
many of the examples you will cite will in fact be enthymemes, ie you 
make an inference which goes beyond the facts available, and assume 
the truth of a missing premis, which later turns out to be false. If 
you had made the assumption explicit, instead of implicit, then you 
can still discover that you were wrong, and acknowledge the resulting 
inconsistency, but now your logic will be monotonic.

There is quite an extensive literature on using this style of 
reasoning in AI planning, by the way, together with a theory of 
minimalization of assumptions. It is incorporated into logical 
programming semantics as 'minimal models' . But all these formalisms 
depend on being able to circumscribe the boundaries relative to which 
one is making the hidden assumptions, and as far as I can see, there 
is nothing on the SWeb which is a plausible candidate for any such 
boundary of circumscription.

>What I fail to see is how I can get out of that perdicament by using 
>monotonic logic.  I would be more confortable with RDF semantics if 
>it did not try to standardize any reasoning at all.  In other words: 
>Let every application provide all the assumtions  that go into its 
>reasoning at its own risk.

The risk is to the user of the assertions, not to the publisher. If I 
publish nonsense and you try to reason with it, it is you, not me, 
who is paying the cost. Hence the need for some rules governing the 
information-exchange process.

>Let that be the warning on the box.
>>>If RDF is really specified like this, then only God will be able 
>>>to write it, because only God will be able to compute all the 
>>>implications of his\her statements forever and ever.
>>Sure, but I don't need to do that, only to guarantee their truth. 
>>And there are lots of facts than can be stated confidently as true 
>>for the forseeable future, eg lists of all the US presidents so far.
>Can you provide me the exact RDF\XML for that ?  I dont know how to 
>apply the "so far" quantifier in RDF.

I meant only that the past presidents of the USA will stay being past 
presidents, for their respective dated terms, into all of future 
history. So a database of such historical, dated, information will 
stay true, if it is ever true.


>Seth Russell

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Received on Monday, 10 February 2003 16:45:33 UTC

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