|
At 8:08 AM -0400 6/26/08, Adrian Walker wrote:
Hi Pat --
I hesitate to debate with such a distinguished logician as
yourself.
Ah, if only it were true...
However, what about SQL? Much of
our commercial and scientific life depends on it, and it undoubtedly
uses negation as "failure to prove".
Are you saying that we should move all commercial databases to a
different query language using classical negation?
Of course not. But not all reasoning is done by querying data
bases. And in any case, the actual logic of negation as failure is
classical, if you describe it carefully. The idea is that in some
cases, one can make an inference from failure to (classical) negation:
failure to find a name in a database of employees enables one to
validly conclude that the person named is not an employee. But
this conclusion itself uses classical negation, notice. That 'not'
simply means that the claim, that whatshisname is an employee, is
false. That is ordinary classical negation. There's no change to
the actual logic when using negation by failure: P and (naf P) are
still in contradiction. What has been added is the extra assumption
that if you don't find something in a certain kind of list, then its
false: a closed world assumption.
You can express this assumption about a database explicitly in
IKL. To say that the list L of names (lists are a datatype in IKL and
can be entirely described by IKL axioms) is closed with respect
to a property P, you can say:
(forall ((p charseq))(if (P (p)) (member p L) ))
And now, if you fail to find <name> in L, so that (not
(member name L)), then you can validly conclude that (not (P (name))),
where the extra brackets around the name means you are talking about
what that name is the name of.
Pat
Cheers, -- Adrian
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
Adrian Walker
Reengineering
On Wed, Jun 25, 2008 at 11:06 PM, Pat
Hayes <phayes@xxxxxxx>
wrote:
At 8:37 PM -0400 6/25/08, Adrian Walker wrote:
Hi John --
Allow me to respond also.
You wrote...
It's important for us to develop Common Logic as the growth
path
for ontologies and to incorporate CL in the Semantic MediaWiki.
Anything currently represented in either the Semantic Web
notations
or relational databases can be mapped to Common Logic. And
the
more compact CL notation is vastly more efficient in storage
space,
transmission time, and computation time than the current Semantic
Web notations.
We should position CL as the foundation for Semantic Web 3.0.
You may like therefore to address Chris Welty's point that CL appears
infeasible for the W3C rule interchange project. In slide 11 of
[1], Chris says:
The CL and IKL approach [is] deprecated: infeasible for this group
[W3C Rule Interchange], as major differences appeared irreconcilable
(e.g. non-mon vs. mon)
He is there referring to a particular approach,
viz. to adopt a highly expressive language into which all rule
languages can be translated, which was used in the IKRIS project which
produced IKL. If however you read on in the same slides, you will find
that the language finally adopted as the initial Rule standard, though
much weaker than CL, in fact is a classical logic with a classical
negation, just like negation in every other logic with a clear
semantics.
The fundamental difficulty seems to
be
That isnt the fundamental difficulty for
RIF.
that CL and IKL have chosen a theoretical
semantics for negation
Its not especially 'theoretical'. It is simply what
negation means in ordinary language. If you say cows are white, and I
say, No, cows are brown; then my "no" says that what you
said is false. That simply is what negation means. This is a
common-sense, pre-theoretical notion of negation. So-called 'negation
as failure' is the theoretical notion, and it only arises from
database theory. The basic snag with negation as failure is that it is
almost always not valid. It is simply wrong. The cases
where you can validly infer, from a failure to prove P, that P is
false, are extremely rare. They only occur in specialized
circumstances in specialized tasks performed by specialists in certain
limited cases. Can you prove that every finite abelian group can be
expressed as the direct sum of cyclic subgroups of prime-power order?
Answer quickly. Suppose, just for the sake of argument, that you
can't. Are you justified in concluding that this is false? Maybe you
had better hedge your bets.
from before the computer era, whereas SQL
and most logic based programming languages use a different meaning for
negation -- one that can also be formalized, e.g. as in [2].
It can be formalized, for sure. It can in fact be
formalized in many different, incompatible, ways. All of them however
make it vividly clear that this is not a generally correct inference
rule.
Pat
Thanks for your thought about this.
-- Adrian
[1] http://ontolog.cim3.net/file/resource/presentation/ChrisWelty_20080612/W3C-Rules-Interchange-Format--ChrisWelty_20080612.ppt
[2] Backchain Iteration: Towards a Practical Inference Method
that is Simple
Enough to be Proved Terminating, Sound and Complete. Journal of
Automated Reasoning, 11:1-22
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
Adrian Walker
Reengineering
On Mon, Jun 23, 2008 at 10:54 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
Peter,
Thanks for posting the audio for Mark Greaves talk. I wasn't
able to log in for the talk, but I read the slides. The
audio
covers some important points that are not in the slides:
http://ontolog.cim3.net/cgi-bin/wiki.pl?ConferenceCall_2008_06_19
The Semantic MediaWiki is very important work, and since
it is
available as open source, we should use it.
But one important point that Mark mentioned is that the reasoning
capabilities of current Semantic Web technology is very weak.
RDF(S), OWL, SPARQL, and RuleML are useful, but weak subsets
of Common Logic.
It's important for us to develop Common Logic as the growth path
for ontologies and to incorporate CL in the Semantic MediaWiki.
Anything currently represented in either the Semantic Web
notations
or relational databases can be mapped to Common Logic. And
the
more compact CL notation is vastly more efficient in storage
space,
transmission time, and computation time than the current Semantic
Web notations.
We should position CL as the foundation for Semantic Web 3.0.
John
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
--
---------------------------------------------------------------------
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
http://www.ihmc.us/users/phayes phayesAT-SIGNihmc.us
http://www.flickr.com/pathayes/collections
--
---------------------------------------------------------------------
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
http://www.ihmc.us/users/phayes
phayesAT-SIGNihmc.us
http://www.flickr.com/pathayes/collections
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01)
|