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Re: [ontolog-forum] Fwd: Ontolog invited speaker session - Dr. Mark Greaves on the Halo Project - Thu 2008.06.19

From: Pat Hayes <phayes@ihmc.us>
Date: Thu, 26 Jun 2008 08:56:02 -0500
Message-Id: <p06230908c4894ba7da03@[192.168.1.2]>
To: "Adrian Walker" <adriandwalker@gmail.com>
Cc: "[ontolog-forum]" <ontolog-forum@ontolog.cim3.net>, "John F. Sowa" <sowa@bestweb.net>, welty@watson.ibm.com, semantic_web@googlegroups.com, "public-semweb-lifesci hcls" <public-semweb-lifesci@w3.org>, semanticweb@yahoogroups.com
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:phayes@ihmc.us>phayes@ihmc.us> 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:sowa@bestweb.net>sowa@bestweb.net> 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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Received on Thursday, 26 June 2008 13:56:45 GMT

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