>Pat,
>
>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
>incomplete.
>
>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
>in.
>
>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)
>Mills
>
>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
>>>formulated?
>>>
>>
>>No.
>>
>>Pat
>>
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>
>Mills Davis
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