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Re: [ontolog-forum] Current Semantic Web Layer pizza (was ckae)

To: Mills Davis <lmd@xxxxxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Mon, 17 Sep 2007 17:25:01 -0500
Message-id: <p06230900c314a7cddf26@[]>
>Oh? And why not?    (01)

Because, in general, there may be infinitely many of them.    (02)

>For example, the Starwars-1 research problem had 
>threat scenarios that went something like:  " We 
>have 300,000 incoming, what's real? what's not? 
>we have 12 minutes to retrain our interceptors. 
>Do we have time for a recursive Lisp algorithm?"
>The answer to the last part of the question was 
>"no".  Recursive algorithms were too slow.    (03)

Quite. One would want to push optimization to its 
limits, probably by writing key portions of the 
code in a low-level language like C++ back when 
SW-1 was being considered. These days however 
optimizing compilers often produce faster code 
than hand-coding, and some very 'high-level' 
languages like Prolog can produce startlingly 
fast runtimes when used properly.    (04)

>The only way to meet the time constraints of the 
>problem was to pre-identify all possible values 
>of all possible variables and system states as a 
>semantic mesh, and then to use incoming sensor 
>data as reality constraints across this jungle 
>gym of reasoning paths in order to ascertain the 
>threat and take action in time.    (05)

Make it into a constraint satisfaction problem, 
in fact. Yes, a good strategy when it is 
possible, which it is only when one has a 
completely worked-out theory for the constraint 
interactions. Such devices are routinely used by 
temporal reasoners, for example. If your problem 
is large but finite - as in this example - and 
*thoroughly* understood and analyzed, and if the 
queries are not complicated (eg have no Boolean 
structure) then one can do such optimizations, 
under the right circumstances. But you asked a 
general question about knowledge in general, and 
the only answer to the general question is, to 
repeat, No.    (06)

>The point is that the impact of all foreseeable 
>reality constraints could be precomputed and the 
>resulting declarative semantic web could be 
>reasoned over in minimum time. Instead of a 
>"no", the answer in this case was "yes".    (07)

Of course the answer will be "yes" in SOME cases. 
If for example the knowledge base is empty.    (08)

>On the other hand, the conclusion of the Star 
>Wars I research was that, while researchers 
>could beat a very complex and comprehensive set 
>of threat scenarios, the military was unlikely 
>to beat the potential enemy (in cold war days, 
>it was usually the Russians) because the enemy 
>could learn and adapt and do something 
>unexpected. In short, they concluded that they 
>could not foresee any and all possible threat 
>scenarios. That is, their knowledge would remain 
>So, to the limits of the knowledge (axioms, 
>etc.) specified, the answer is "yes". I can 
>precompute the implications of forward and 
>backward chaining axioms.    (09)

There are trivial counterexamples. Here is one 
(stated in pseudo-english: choose your favorite 
formalization):    (010)

Nothing is larger than itself.
If x is larger than y and y is larger than z, then x is larger than z.
Everything has at least one thing larger than it 
and one thing it is larger than.
At least one thing exists.    (011)

It follows that infinitely many things exist 
which are larger, and infinitely many which are 
smaller, than the last-mentioned thing. Now, to 
generate ahead of time all the possible 
consequences of a new fact added to this would 
require infinite time and infinite memory 
capacity, in general. So it can't be done.    (012)

BTW, there are also finite cases where the 
closure can be pre-computed, but nevertheless may 
fail to have all the answers in it, if one is 
allowed to make queries containing disjunctions 
(or which use concepts whose definitions contain 
disjunctions.) Even in OWL-DL cases like this 
arise. There is an extensive literature on this 
topic. In general, pre-computing axiom 'closures' 
to reduce inference to look-up can be done only 
in very restricted cases. (It works for RDF and 
RDFS - see http://www.w3.org/TR/rdf-mt/#rules - 
but not for OWL.)    (013)

>  (The trade here is space vs time.)
>In terms of reality, however, it seems that our 
>"knowledge" is not "truth" but more a system of 
>constraints.    (014)

A system of constraints can be true. All 
knowledge can be viewed as a system of 
constraints, in fact.    (015)

>More often than not it is partial and incomplete    (016)

almost always it will be so, yes.    (017)

>, and likely to be in conflict or competition 
>with other knowledge or values that we believe 
>Permit me to wax for a moment. I think the 
>really interesting stuff of reasoning (e.g., 
>questions where lives are on the line, questions 
>of guilt or innocence, questions of ethics, 
>questions about what is the best product design, 
>or best course of action for a business, 
>questions of public policy, or career choices) 
>always involve more than logical consistency. 
>They involve trade-offs and values. Often there 
>is no "right" answer. Logic is just a tool.    (018)

You are confused about the role of logic. Logic 
does not purport to give you the "right" answer; 
and of course meaningful decisions involve more 
than logical consistency. Logic only provides the 
connections between assertions, not any guarantee 
as to their veracity or appropriateness. It does 
not follow however that logic, and logical 
consistency, should be abandoned or rejected.    (019)

In any case, this has nothing at all to do with the topic of this thread.    (020)

Pat    (021)

>On Sep 17, 2007, at 12:58 PM, Pat Hayes wrote:
>>>Wouldn't the impact of all possible 
>>>informational variables be (pre)computable at 
>>>the time the backward/forward axiom was 
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><mailto:lmd@xxxxxxxxxxxxxx>lmd@xxxxxxxxxxxxxx    (022)

IHMC            (850)434 8903 or (650)494 3973   home
40 South Alcaniz St.    (850)202 4416   office
Pensacola                       (850)202 4440   fax
FL 32502                        (850)291 0667    cell
phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes    (023)

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