Hi Len,

You wrote:

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.

I don't follow your reasoning on this one. Why would two RDBs have a
different reasoning mechanism, situation description, or otherwise any
difference at all between the two RDBs? I am somehow missing your meaning and
yet I think you have something important to say here. Can you state it more clearly
please?

HTH,

-Rich

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

-----Original Message-----

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Len Yabloko

Sent: Sunday, December 27, 2009 6:56 PM

To: [ontolog-forum]

Subject: Re: [ontolog-forum] blogic iswc keynote

Thank you to everyone for very interesting discussion

>

>Chris,

>

>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"?

>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.

I think so too.

>

>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

>different.

>

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.

>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

>(http://www.amazon.co.uk/Inventing-Temperature-Measurement-Scientific-Philos

>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

>explanation.

>

>Regards,

>Chris

>

>

>

>> -----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

>> mathematics.

>>

>> 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

>> intractability.

>> >

>> > 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

>> are.

>>

>> > 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.

>>

>> -chris

>>

>>

>>
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