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At 4:05 PM -0400 6/26/08, Chimezie Ogbuji wrote:
Just a quick comment. Pat H.
wrote
[[
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.
]]
I would disagree about this case being the exception. Negation
as failure can be validly used to infer from a failure if the data is
controlled (which is especially the case with well-designed
experiments where it would be irresponsible to to do
otherwise).
What are you referring to by "well-designed
experiments"?
If a clearly-defined protocol is
used as part of the data collection process (for example, only assert
P if P is known)
OK, but that does not ensure that if P is not asserted,
then it is known to be false. In fact, rather the
opposite.
, then you can make valid inferences
about missing content
You can make such inferences validly only when you have
some reason to suppose that if the proposition were true, the content
would not be missing. I don't mean to deny that such circumstances do
exist, in some cases with an explicit warrant for the entailment, but
they are certainly not the usual case. The usual case is that your
knowledge is incomplete. Our knowledge of almost everything is
incomplete.
without the burden of classic negation,
which requires a significant amount of effort
Nonsense. There is no 'burden' of classical negation. Negation IS
classical negation. If you conclude that P is false, and express this
using a negation connective, you are using classical negation. (If
your *conclusion* from a failure to prove P is that P is not proven,
then your reasoning is completely classical also; but then you are
only concluding failure, not negation from failure.)
(either having a large amounts of
assertions about class disjointedness, etc. or requiring explicit
assertions about the absence of data)
You have to say what is true in order to draw reliable
conclusions from it. This can be done in tedious ways or, with the
right notations and conventions, more compactly. You are reacting
against some of the more tedious notational results of using simple
textbook logics. But if you want to be able to infer, from the fact
that something is in a class A, that it is not in another class B,
then you must have some way to know that A and B are disjoint.
Because if they aren't, that conclusion is not valid. No amount
of grumbling about classical negation is going to get over that basic
fact. If you want to seriously propose that we should adopt as a
logical principle that all classes with different names are
disjoint, then tell me how you will discuss subclass
relationships.
to ensure that you can prove
that P is false.
You have to know somehow. You might just know because
someone told you, or because you know that if it were true then you
would have it recorded, and you don't. But you have to know
this. You can't just guess it or hope that it will be true, and call
the result a 'logic'.
Pat
On 6/25/08 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 <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 <http://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
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