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Re: [ontolog-forum] Categorical Views of a Universe

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Jawit Kien <jawit.kien@xxxxxxxxx>
Date: Fri, 28 Jan 2011 11:18:14 -0600
Message-id: <AANLkTikYrPCPSyCK5bhq-DjeetcFZ-q7vrZfJcJ+B600@xxxxxxxxxxxxxx>
The idea that Dr. Sowa mentioned, about adding detail can make a
theory more specialized makes sense to me.  It is certainly the case
that if I had some axioms talking about a situation, such as "getting
wet outdoors", that adding more axioms could make the theory more
specialized.    (01)

For example: (getting wet outdoors ontology)    (02)

You get wet
          if you stand outdoors
          when it is raining.
You get wet
       if you stand outdoors
       and you don't have an umbrella
       when it is raining.    (03)

if you add the a conjunctive detail to axiom 2:
You get wet
        if you stand outdoors
        and you don't have and umbrella
        and you are not standing under the eaves of a house
        when it is raining    (04)

you can see that this makes the ontology more specialized.
It also increases the need to have supporting vocabulary
and consistent definitions of terms, and relations to be able
to express the added conjunctive detail.    (05)

On 1/27/11, Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx> wrote:
> John you stated below:
>
>   1. Adding detail (axioms, constraints) makes a theory more
>
>      specialized, and it can sometimes create an inconsistency.
>
>
>
>   2. Deleting detail makes a theory more generalized, and it
>
>      can never make a consistent theory inconsistent.
>
>
>
> In the first case, adding a conjunctive clause to inhibit the subclass that
> clause designates would add detail, and would in complex databases further
> reduce the number of individuals predicated by the class expression.  That
> can be useful, but the only inconsistency that can crop in, AFAIK, is a
> dropped reference - a dangling reference some call it.  Is there another
> source of inconsistency you have in mind?    (06)

What do you mean when you say a conjunctive clause can inhibit a subclass
that is designated by a clause ?    (07)

>
>
>
> Deleting a conjunctive clause in a theory's designation expression might
> increase the number of individuals covered by the updated expression.  New
> facts and rules, added to a class of facts and rules, should be able to
> cause inconsistencies by asserting previously negated facts and rules as
> should be possible in most practical applications.
>    (08)

Assuming a theory is a group/set of axioms, what do you mean by a theory's
designation expression ?    (09)

I presume when you say an expression covers a number of individuals, that you
are saying that if you use the logical expression in a statement
(for example:)    (010)

"for all individuals designated by a set of variables,
such that the logical expression using those variables is true "    (011)

that any individuals which are matched to those variables are the ones
covered by that logical expression.    (012)

so if you delete a conjunctive clause in that logical expression,
you are increasing the count of individuals which are matched.    (013)

Is this what you mean ?    (014)

Thanks,
JK    (015)


>
>
> JMHO,
>
> -Rich
>
>
>
> Sincerely,
>
> Rich Cooper
>
> EnglishLogicKernel.com
>
> Rich AT EnglishLogicKernel DOT com
>
> 9 4 9 \ 5 2 5 - 5 7 1 2
>
>
>
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: Thursday, January 27, 2011 1:37 PM
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Categorical Views of a Universe
>
>
>
> On 1/27/2011 2:56 PM, Ron Wheeler wrote:
>
>> We have tools (Maven) that let describe the dependencies and the
>
>> compatibility between libraries and control how a program (or library)
>
>> is built, assembled and deployed.
>
>> We have repositories(Nexus and others) that hold many versions of the
>
>> same library.
>
>> We have forks of libraries that are mostly the same but get different
>
>> identifiers.
>
>> We use "GroupId", "ArtifactID" and "Version number" (GAV) to uniquely
>
>> identify a library.
>
>
>
> Any or all of those features are completely compatible with the idea of
>
> organizing ontologies in a hierarchy.
>
>
>
>> Assumptions about upwards compatibility are commonly made but are not
>
>> guaranteed and the person defining the dependency has to carefully
>
>> consider the version or version range that the will use.
>
>
>
> This is an area where the theory of lattices and software based
>
> on it (of which a great deal exists) can provide more info about
>
> the interrelationships and help test and verify the claims.
>
>
>
> Some principles are simple and guaranteed:
>
>
>
>   1. Adding detail (axioms, constraints) makes a theory more
>
>      specialized, and it can sometimes create an inconsistency.
>
>
>
>   2. Deleting detail makes a theory more generalized, and it
>
>      can never make a consistent theory inconsistent.
>
>
>
> Others may require more testing (which could, in the worst case
>
> be undecidable).   But trying to do the test can never hurt --
>
> the worst it might do is to run an unused computer for a whole
>
> weekend without reaching a conclusion.  That doesn't prove that
>
> the system is consistent or inconsistent, but it could be a
>
> warning.
>
>
>
> John
>
>
>
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>    (016)

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