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 <http://www.reengineeringllc.com>www.reengineeringllc.com
Shared use is free
Adrian Walker
Reengineering
On Wed, Jun 25, 2008 at 11:06 PM, Pat Hayes
<<mailto:[EMAIL PROTECTED]>[EMAIL PROTECTED]> 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>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 <http://www.reengineeringllc.com>www.reengineeringllc.com
Shared use is free
Adrian Walker
Reengineering
On Mon, Jun 23, 2008 at 10:54 PM, John F. Sowa
<<mailto:[EMAIL PROTECTED]>[EMAIL PROTECTED]> 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>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
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