Thank you to everyone for very interesting discussion
>I think there is quite an important point at stake here.
>The real issue seems to me not whether one can pick holes in the details of
>John's points (however much fun that is!), but whether the overall substance
>has any meat on it.
>That is why if I were to accept, for the sake of this argument, your
>dissection of the points below, then I would feel you still do not get us to
>quite where you would want us to be. That something relevant has been missed
>out. (And that you have not been charitable enough to John.)
>I assume it is a relatively un-contentious point that most business system
>building practitioners would be surprised to hear that (logical)
>intractability is anything other than a theoretical problem when building
>systems. Many of the IT architects, designers and programmers I know would
>not even recognise the term. (If anyone disagrees, please let us know.) So
>how come they miss such an obvious problem? Maybe, at a practical level it
>is not a genuine category of problem?
I don't disagree, but as a practitioner would like to add that even long
periods of not recognizing the term or the theoretical problem does not always
make it not a genuine category of problem. It is true - some very fundamental
problem like "three body" problem or "uncertainty" principle did not preclude
very successful engineering. Nor did general undecidability of FOL. But sooner
or later engineering does come to a point where the problem must be dealt with.
And when it does - the entire body of practical acumen can become an obstacle
to further progress. Is that what you call "an illusion of validity"? (01)
>Interestingly the google test on "business systems intractability" gives
>results where intractability is about complexity rather than logic.
>Now maybe you can argue that business system practice is not relevant. That
>for KE on the semantic web we are (from a practical point of view) in a new
>situation. And you can see that in this situation (unlike with business
>systems) intractability becomes a problem. Maybe that is the way the
>argument should go. (02)
I think so too. (03)
>However, I did not see you making that argument. And when/if you do, it
>would need to be a strong enough to give practical reasons why the
>heuristics that have grown up over the last half century when building
>business systems cannot be applied successfully in some way to the semantic
>web. I suppose this would involve an explanation of why the two are so
I think the main point of contention in this discussion had originated in
questioning applicability of expressive languages (like SQL) to reasoning over
semantic web. And indeed there are many similarities between reasoning in RDB's
and SW. But there is one crucial difference - RDB's are assumed to be correctly
representing the state of the business application. If we remove this
assumption then most of engineering practices around it will fail. I also
believe that this is a stronger assumption than the "closed world assumption"
which only assumes the database to be complete. Together completeness and
correctness of RDB make possible most of practical engineering approaches.
Interestingly, if you take two difference RDB's and try to reason over both at
the same time - you will find a lot of queries un-decidable. This why
practitioners will avoid this at any cost. They would rather merge the datasets
repeatedly (or endlessly which would cost astronomical amounts of money).
Unfortunately, the web can not be continuosly merged. As usual engineers did
find a way around and invented a search engine which is the closes you come to
merged global database index. However, it clear to everyone that this solution
is not satisfactory and temporary. (05)
>My guess is that business systems engineers have developed heuristics for a
>range of problems where intractability gets bundled in with a large number
>of other things and so is not singled out. This is not a new idea. Herbert
>Simon (and design science) makes a similar point. Interestingly I saw from
>the outside something similar in action a year or so ago when Hasok Chang
>ophy/dp/0195171276 - who I have mentioned before) was explaining to
>engineers at the Royal Institute of Engineers how scientists develop
>temperature measurement techniques to avoid awkward complications. The
>engineers did not get it as these awkward situations were 'standard' for
>them - and the science was non-standard engineering - as they faced these
>problems in real life.
>My guess (and it is no more than a guess) is that while rules of inference
>(and so intractability) are part of the framework, there are a number of
>other levels in the framework and all of these contribute to how
>practitioners address the problem. And it seems to me that when this is all
>in place practitioners have not found logical tractability a useful category
>(let me know if my sample is skewed). Now maybe they should, but that
>requires an argument that shows their current stance is not optimal.
>However, all of this still leaves room for you to argue that the KE/semantic
>web framework is different.
>CM>> Seriously? Only professional mathematicians and logicians are capable
>> of conceiving, say, the traveling salesman problem?
>Interesting that you chose this example. For Simon and his ilk, this is an
>example par excellence of design, where the heuristics for getting a
>solution work around a complex problem (which may be intractability or just
>difficult) rather than worry about dealing with it. Where practice is driven
>by economics rather than 'truth'. I guess they would argue this is the
>difference between theory and practice.
>I think this needs some more explanation (and I do not have a good one yet)
>so if you have the arguments/explanations that show it is practical to
>tackle intractability more directly, I would be really interested.
>Otherwise, I guess we have to accept this is something waiting for a good
>> -----Original Message-----
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher Menzel
>> Sent: 23 December 2009 18:47
>> To: [ontolog-forum]
>> Subject: Re: [ontolog-forum] blogic iswc keynote
>> On Dec 18, 2009, at 1:32 PM, "John F. Sowa" <sowa@xxxxxxxxxxx> wrote:
>> > I was talking about the many different ways of using a statement in
>> > a logic, such as FOL. Theorem proving is only one use among many.
>> > In fact, it is probably very far down the list of things one might
>> > want to do with logic. For example,
>> > 1. Communicate some information -- i.e., transmit an assertion.
>> Whose implications for your own knowledge base you might well want to
>> calculate. Calculating implications is just theorem proving.
>> > 2. Check whether somebody's assertion is consistent with the
>> > facts -- i.e., evaluate truth in terms of a specific model.
>> But in order to be consistent with the facts a statement must be
>> consistent simpliciter and the problem of consistency simpliciter is
>> undecidable. Hence, so too is the question of whether a statement is
>> consistent with the facts. Consistency checking, of course, is just
>> another name for theorem proving.
>> So far your list is illustrating my point.
>> > 6. Check whether a given statement is true of all possible models
>> > -- prove a theorem.
>> Well, that's kind of a misleading way of putting it, since it is
>> impossible actually to check all possible models (as you well know).
>> Rather we (in effect) look for a proof and if we find one, then, of
>> course, it *follows* in virtue of soundness that the statement is true
>> in all possible models.
>> > Point #6 happens to be a very high priority among logicians who think
>> that the primary use of logic is to form the foundation for
>> John, I know this is one of your favorite hobby horses, but
>> irrespective of its importance to logicians, point #6 is surely a (not
>> THE, just A) critical component in the overall vision of the semantic
>> web, as already illustrated in points 1 and 2 above. If I am going to
>> draw on your knowledge base, I will want to know that your information
>> is consistent with mine and I will want to be able to calculate the
>> implications of doing so.
>> >>> JFS> The paternalistic approach assumes that all users are trying
>> to prove a theorem that is valid for all possible models. But most
>> people who ask a question are only interested in a specific model,such
>> as the current DB.
>> >> CM> This isn't clear to me at all. If I'm just trying to describe a
>> certain conceptual domain like, say, human physiology...
>> > First of all, physiology is an experimental science. In the
>> development of that science, the most important use for any kind of
>> precise notation (say ordinary language expressed in a way that could
>> be translated to FOL) is to state observations and form
>> generalizations. That is communication (#1 on the list above), fact
>> checking (#2), and induction (#3).
>> >> CM> ... it doesn't seem to me that any inferencing is done vis-á-vis
>> any sort of fixed finite model.
>> > I have no idea what kind of inferencing you are talking about.
>> Physiologists aren't the kind of people who state anything in axioms.
>> Then I have no idea what *you* are talking about. Of course
>> physiologists don't state things in terms of axioms. Isn't that
>> exactly the job of an ontologist? Isn't the whole idea here to get
>> such information represented formally in terms of a first-order
>> representation language?
>> > They are much more likely to be doing #1, #2, #3, #4, and #5 above
>> than #6.
>> At least two of which, as noted, entail #6.
>> > Even physicists state in a tone of derision that they "don't do
>> axioms" -- that is in response to things like von Neumann'saxioms of
>> quantum mechanics.
>> And ontologists don't "do" cloud chamber experiments. How is this
>> relevant? Of course physicists "don't do axioms". They are doing
>> physics; they are not trying to implement the Semantic Web.
>> Ontologists are, so they "do" axioms.
>> > CM> which, if expressed in full FOL, raises the possibility of
>> > That possibility is only slightly more likely than the chance that
>> the world will end tomorrow.
>> Huh? You're saying that every "real world" problem is solvable in
>> polynomial time?
>> > Nobody but a professional mathematician or logician is even capable
>> of "thinking" of an intractable statement, let alone worrying about
>> whether it can be proved.
>> Seriously? Only professional mathematicians and logicians are capable
>> of conceiving, say, the traveling salesman problem? You really don't
>> think that's a real problem for, say, people working in logistics? And
>> are you really unaware of the problems of intractability in
>> computational biology or molecular dynamics (e.g., protein folding)?
>> How about n-body problems in physics and astronomy?
>> > Please note that mathematicians have been using FOL for millennia.
>> > They were blissfully unaware of computational complexity or
>> > undecidability. Yet it never caused the slightest problem for them.
>> Well, of course -- those problems didn't *exist*. There was no formal
>> model of computation prior to Turing, and no computers with which to
>> try to solve mathematically formulable problems, so there were no
>> mathematical problems of complexity and undecidability. But now there
>> > All the FOL statements that Whitehead and Russell stated in the
>> _Principia Mathamtica_ can be proved in a fraction of a second with
>> modern theorem provers.
>> I am frequently amazed at how fast Prover9 and its ilk are able to
>> solve problems involving multiply-nested quantifiers -- more so because
>> I had once programmed a tree-based theorem prover on my own as a
>> programming exercise that was mostly miserable at solving such
>> problems. However, this is really neither here nor there. W&R were
>> not interested in problems that give rise to intractability. All of
>> their theorems are highly amenable to automated solution (obviously).
>> > CM> I'm not saying [intractability] can't be managed -- obviously, it
>> can, if only by putting temporal bounds on searches for proofs and
>> countermodels. But that there might be a need to do so if one uses full
>> FOL does need to be expressed.
>> > Yes, such checks should be part of the development methodology.
>> Really? Why? I thought intractability is just a concern for
>> professional mathematicians, logicians and other out of touch ivory-
>> tower denizens?
>> I agree with you on most matters, John, but your views on
>> intractability mystify me.
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