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Re: [ontolog-forum] The Open world assumption shoe does not always fit - was: RE: Fwd: Ontolog invited speaker session - Dr. Mark Greaves on the Halo Project - Thu 2008.06.19

From: Pat Hayes <phayes@ihmc.us>
Date: Fri, 27 Jun 2008 11:31:13 -0500
Message-Id: <p06230901c48ac2e52427@[]>
To: "[ontolog-forum] " <ontolog-forum@ontolog.cim3.net>
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, "Obrst, Leo J." <lobrst@mitre.org>, "Adrian Walker" <adriandwalker@gmail.com>
At 9:37 AM -0400 6/27/08, Adrian Walker wrote:
>Pat, John, Chimeze and all --
>Illuminating discussion.

FWIW, all my replies to three of the groups in your CC line get 
rejected, so somebody is only getting half the story :-)

>Two points:
>1. If you move to from SQL-like NAF reasoning, to full FOL with 
>closure statements at the meta level, you may also be moving from 
>low order polynomial computational complexity to exponential, or 
>even into the undecidable region.

Well, maybe, but I don't see how. The actual reasoning process would 
be very similar, its really only the semantics that changes. Thats 
assuming that you have the metadata to hand, of course: if you have 
to do arbitrary FO reasoning to extract the relevant metadata, then 
yes, that is theoretically undecideable.

I'm not all that worried about worst-case results like this, though. 
The worst-case for RDF is already NP-complete, but that doesn't seem 
to impact actual practice. Any useful general-purpose ontology 
language is going to be undecideable.

>  A succinct paper on this issue would be good to have.
>2.  Some of the worry about SQL-NAF possibly leading to wrong 
>conclusions appears to come from the assumption that the intended 
>real world meaning of things like p133(?X,?Y) is nowhere documented.

Being documented isnt the point: it has to be accessible to the 
actual reasoning.

>  However, if you attach English sentences to  predicates [1], and 
>hide the predicates themselves, then answers from your deductions 
>can be sentences like
>  "Assuming that we have all the relevant data, as of 20080627, Pat 
>does not work for IBM". 
>Then, there's no way for the English documentation to get separated 
>from the logic, because authors and users deal only with the 
>executable English.  English explanations can also help to document 
>how the answers are arrived at.

Sure, but how does the reasoning engine use those documentations?


>These two points may also be relevant for RDF [2].
>Thanks for your further thoughts.
>                                          -- Adrian
>[1]  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
>On Fri, Jun 27, 2008 at 1:34 AM, John F. Sowa 
><<mailto:sowa@bestweb.net>sowa@bestweb.net> wrote:
>I'd just like to summarize a few points, which reinforce the claim I
>made earlier:  There is an open-ended number of different variations of
>nonmonotonic logic, and it's impossible to adopt a one-size-fits-all
>solution for nonmonotonic logic.
>To paraphrase Tolstoy, every happy logic (i.e., classical) is happy
>in the same way, but every unhappy logic (nonmonotonic) is unhappy
>in its own way.
>The solution I recommend is to treat all nonmonotonic operators
>as metalevel predicates about some proposition or some proof.
>In IKL (or any other logic that supports metalevel statements),
>predicates such as is-provable(p), is-not-provable(p), is-default(p),
>has-fuzzy-value(p,x), or probability-of(p,x), are metalevel
>statements about some proposition p.
>If you assume a closed world (such as a database of all airline
>reservations or all employees), you can write metalevel axioms
>saying that anything not provable is false.  If you have an open
>world with incomplete information, you can write metalevel axioms
>that say what to do about such cases.  If you have a mixed DB
>with complete info about some things and incomplete info about
>other things, you can write axioms to say what to do in each case.
>Professional database administrators and authors who have studied
>the issue for a long time (such as Chris Date), know how to
>design and use DB systems in order to achieve predictable
>results.  Many casual users manage to avoid trouble by using
>a database as a convenient way of storing and accessing positive
>data, and they assume that the "not" operator is shorthand for
>"not found".
>In short, a logic with a classical semantics, such as CL or IKL,
>is an ideal foundation for defining the semantics of any and every
>version of nonmonotonic logic that has ever been invented.
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Received on Friday, 27 June 2008 16:31:51 UTC

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