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Re: [ontolog-forum] Logic, Datalog and SQL

To: "Adrian Walker" <adriandwalker@xxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 8 Feb 2007 15:30:56 -0600
Message-id: <p06230922c1f13f1fd5e4@[]>
>Hi Ed --
>Actually, the thought was that since the 
>closed/open world negation debate generates so 
>much heat, an encyclopedia entry for logic and 
>ontologies could shed some light on the matter 
>by clearly setting out the arguments on both 
>sides.    (01)

Even treating this as a binary debate with 
'sides' is an oversimplification. There are two 
(in fact, rather more) kinds of reasoning. They 
both have their uses. Anyone who argues that one 
alone is enough for all purposes is evidently 
wrong. The right way to pose the debate is how to 
find ways of ensuring that the appropriate 
inference method is used in the appropriate 
circumstances.    (02)

It should not be thought of as a conflict between 
kinds of negation. There really is only one 
notion of negation. So-called 'closed world 
negation' is the application of an inference rule 
which uses this (classical) negation in its 
conclusion. When you don't find the entry in the 
database and conclude that the person is NOT an 
employee, that NOT in the conclusion isn't 
negation-as-failure: it is simply negation. The 
inference process that led to it *inferred* 
negation *from* failure. Or, on the other hand, 
if what you concluded is not that the person is 
NOT an employee, but instead that his name is not 
listed in the database, then you are using 
classical logical reasoning, since this 
conclusion is classically valid. And as stated, 
it still uses classical negation ("..NOT listed 
in the ..."). In fact, every occurrence of "not" 
in this paragraph is classical negation, the only 
negation there is.    (03)

I suspect this muddle has arisen in part from the 
unfortunate term "negation-as-failure". If we had 
called this "negation-from-failure" it might have 
been clearer. BTW, this can be described directly 
in IKL:    (04)

(forall (KB R)(iff
(Closed XB R)
(forall ((s charseq)) (if  (not (member s KB) (not (R (s)) ) ))
))    (05)

using the IKL convention that any character 
string is also a zero-ary function whose value is 
the denotation of the string when it is used as a 
name.    (06)

>   The entry would not need to resolve the issue, 
>just clarify it.  Perhaps with examples about 
>where each kind of negation works best.
>You wrote...
>One can, for certain "instantaneous" inferences, assume that the universe is
>finite and consists only of things recorded in the current information base.
>But to account for the evolution of that information base over time, one
>obviously cannot make that assumption.  And one has to step very carefully
>through the swamp that is created when these notions get mixed.
>Actually, there appears to be a rather easy way 
>out of the swamp, at least in principle and for 
>some purposes:
>   * Associate, with each chunk of information, a 
>list of start times and end times.
>   * Never delete any information, just grow the 
>time lists, and add new "timed" information
>   *  Associate with any answer to a question 
>about the information, the time point(s), or 
>time period(s), for which the answer is valid.
>   *  When querying, use closed world negation at will.
>Storage intensive, but perhaps worthwhile.  Or am I overlooking something?    (07)

I don't see how this helps. Many data sources are 
complete enough for certain kinds of data to be 
treated by closed-world reasoning, but many also 
are not. The Web as a whole is not. Adding times 
does not help with this at all.    (08)

Pat    (09)

>                                          Cheers,  -- Adrian
>Internet Business Logic (R)
>A Wiki for Executable Open Vocabulary English
>Online at <http://www.reengineeringllc.com>www.reengineeringllc.com
>                                 Shared use is free
>Adrian Walker
>Phone: USA 860 830 2085
>On 2/8/07, Ed Barkmeyer <<mailto:edbark@xxxxxxxx>edbark@xxxxxxxx> wrote:
>Adrian Walker wrote:
>>  Actually, if there is to be a new Wikipedia or other encyclopedia entry on
>>  logic for ontologies, it should summarize the ongoing debate between the
>  > "closed" and "open" world negationist camps.
>I would welcome that, but I wonder how many rounds it will take to get a
>version that is acceptable to most of the parties involved.
>It is my impression that there are at least 3 importantly different models of
>the "closed world", and they probably relate to what kind of inferences the
>"camp" wants to make.  Further, there are several problems that arise when the
>closed worlders need to mix "closed" concepts and "open" concepts.
>One can, for certain "instantaneous" inferences, assume that the universe is
>finite and consists only of things recorded in the current information base.
>But to account for the evolution of that information base over time, one
>obviously cannot make that assumption.  And one has to step very carefully
>through the swamp that is created when these notions get mixed.  That is why,
>Michael Kifer, for example, says that all rules languages are programming
>languages.  They model a carefully chosen inferential procedure.
>As to Adrian's examples:
>>  Almost all uses of databases
>>  in our everyday life rely on things like "if it's not in the catalog we
>>  don't stock it",
>This is probably a business rule.  It is true because, like Jean-Luc Picard,
>we "make it so".
>>  "if no flight number to Podunk is in the database, then
>>  there is no flight to Podunk"
>that we can do anything about.
>The speaker doesn't actually care whether there is a flight to Podunk; he is
>focussing only on knowledge that affects HIS behavior.  But knowledge that
>does not affect his behavior might very well affect the behavior of some other
>person who has access to the same information.
>>  so we should not ignore closed world
>>  usage of
>>  databases just because the clasical logicians never wrote about it.
>I'm not a crazy evangelist for monotonicity, either.  I only point out that
>closed world systems are designed for a particular purpose, and in general,
>you cannot use them safely for inferencing for any other purpose.
>Edward J. 
>Barkmeyer                        Email: 
>National Institute of Standards & Technology
>Manufacturing Systems Integration Division
>100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
>Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694
>"The opinions expressed above do not reflect consensus of NIST,
>   and have not been reviewed by any Government authority."
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>    (010)

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