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At 9:37 AM -0400 6/27/08, Adrian Walker wrote:
Pat, John, Chimeze and all --
Illuminating discussion.
FWIW, all my replies to three of the groups in your CC line get
rejected, so somebody is only getting half the story :-)
Two points:
1. If you move to from SQL-like NAF reasoning, to full FOL with
closure statements at the meta level, you may also be moving from low
order polynomial computational complexity to exponential, or even into
the undecidable region.
Well, maybe, but I don't see how. The actual reasoning
process would be very similar, its really only the semantics that
changes. Thats assuming that you have the metadata to hand, of course:
if you have to do arbitrary FO reasoning to extract the relevant
metadata, then yes, that is theoretically undecideable.
I'm not all that worried about worst-case results like this,
though. The worst-case for RDF is already NP-complete, but that
doesn't seem to impact actual practice. Any useful general-purpose
ontology language is going to be undecideable.
A succinct paper on this issue
would be good to have.
2. Some of the worry about SQL-NAF possibly leading to wrong
conclusions appears to come from the assumption that the intended real
world meaning of things like p133(?X,?Y) is nowhere
documented.
Being documented isnt the point: it has to be accessible to the
actual reasoning.
However, if you attach English
sentences to predicates [1], and hide the predicates themselves,
then answers from your deductions can be sentences like
"Assuming that we have all the relevant data, as of
20080627, Pat does not work for IBM".
Then, there's no way for the English documentation to get separated
from the logic, because authors and users deal only with the
executable English. English explanations can also help to
document how the answers are arrived at.
Sure, but how does the reasoning engine use those
documentations?
Pat
These two points may also be relevant for RDF [2].
Thanks for your further thoughts.
-- Adrian
[1] Internet Business Logic
A Wiki and SOA Endpoint for Executable Open Vocabulary English over
SQL and RDF
Online at www.reengineeringllc.com Shared use is free
[2] www.reengineeringllc.com/demo_agents/RDFQueryLangComparison1.agent
Adrian Walker
Reengineering
On Fri, Jun 27, 2008 at 1:34 AM, John F.
Sowa <sowa@xxxxxxxxxxx>
wrote:
Folks,
I'd just like to summarize a few points, which reinforce the claim
I
made earlier: There is an open-ended number of different
variations of
nonmonotonic logic, and it's impossible to adopt a
one-size-fits-all
solution for nonmonotonic logic.
To paraphrase Tolstoy, every happy logic (i.e., classical) is
happy
in the same way, but every unhappy logic (nonmonotonic) is unhappy
in its own way.
The solution I recommend is to treat all nonmonotonic operators
as metalevel predicates about some proposition or some proof.
In IKL (or any other logic that supports metalevel statements),
predicates such as is-provable(p), is-not-provable(p),
is-default(p),
has-fuzzy-value(p,x), or probability-of(p,x), are metalevel
statements about some proposition p.
If you assume a closed world (such as a database of all airline
reservations or all employees), you can write metalevel axioms
saying that anything not provable is false. If you have an
open
world with incomplete information, you can write metalevel
axioms
that say what to do about such cases. If you have a
mixed DB
with complete info about some things and incomplete info about
other things, you can write axioms to say what to do in each case.
Professional database administrators and authors who have studied
the issue for a long time (such as Chris Date), know how to
design and use DB systems in order to achieve predictable
results. Many casual users manage to avoid trouble by using
a database as a convenient way of storing and accessing positive
data, and they assume that the "not" operator is shorthand
for
"not found".
In short, a logic with a classical semantics, such as CL or IKL,
is an ideal foundation for defining the semantics of any and every
version of nonmonotonic logic that has ever been invented.
John
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