Re: [ontolog-forum] Fwd: Ontolog invited speaker session - Dr. Mark Grea

[Pat Hayes <phayes@xxxxxxx>]

At 9:44 AM -0400 6/26/08, Patrick Cassidy wrote:

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> Pat ­
>    Is there a logic defined
> somewhere that includes both types of negation as logical operators?:
>  ?NotProven¹ and ?ProventNot¹?

Its certainly been suggested, and Im sure someone has defined it, but I don't have actual pointers.  But IMO this is a losing idea. First, classical negation isn't "provenNot", its just plain Not. Nothing in the negation truthtable says anything about provability. Second, NAF isn't a different connective, and trying to make it into one just gets everything muddled. If you use NAF, the conclusion you reach is properly expressed as a simple negation: "Joe" isn't in the list, so Joe is not an employee. That's ordinary classical negation in the conclusion. Whats special about NAF isn't the final assertion, its the way that you come to believe it (or, if you take the goal-directed ass-backwards view of most query or LP systems, its the way you set out to prove it.)

PatH

>  
> Pat
>  
> Patrick Cassidy
> MICRA, Inc.
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>  
> From:
> ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> Pat Hayes
> Sent: Wednesday, June 25, 2008 11:06 PM
> To: Adrian Walker
> Cc: semanticweb@xxxxxxxxxxxxxxx; [ontolog-forum];
> public-semweb-lifesci hcls; semantic_web@xxxxxxxxxxxxxxxx;
> welty@xxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Fwd: Ontolog invited speaker
> session - Dr. Mark Greaves on the Halo Project - Thu
> 2008.06.19
>  
> 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
> > > _________________________________________________________________
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