# Re: Equality and subclass axioms

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Sun, 26 Nov 2000 14:23:33 -0500

Message-Id: <20001126142333W.pfps@research.bell-labs.com>
```From: Jim Hendler <jhendler@darpa.mil>
Subject: Re: Equality and subclass axioms
Date: Sat, 25 Nov 2000 22:59:44 -0500

> Ian-
>   Here's my worry, which is controllable, but definitely worth
> thinking about.  You, being a rational person, come about with a rule
> that says triangles are three-sided things.  I, being an irrational
> person, have an axiom stating triangles are 4-sided.  We both use if
> and only if rules.  Some web crawler comes, scrapes both of our rules
> into the same knowledge base -- and then what happens?  Do we get two
> kinds of triangles or no kinds of triangles.  Obviously, no model can
> allow triangles that are  both  three and four-sided - so I would
> assume by throwing in my irrational axiom I've somehow "negated"
> yours.  Notice if we're not using If and only if, this problem
> doesn't come up (i.e. IF three sides and IF 4 sided can concurrently
> occur).

I don't understand how going from if definitions to iff definitions changes
this worry.  If I believe that all triangles have three sides (an if
definition), perhaps because Ian says so, and I also believe that all
triangles have four sides (another if definition), perhaps because Jim says
so, then there will be no objects that satisfy my beliefs about triangles
and if I try to state that some object is a triangle, I will get an
inconsistency.   The situation appears to be completely analogous with iff
definitions---again there will be no objects that satisfy my beliefs about
triangles and if I try to state that some object is a triangle, I will get
an inconsistency.

Certainly there are problems with obtaining information from several
sources.  Certainly there needs to be mechanisms to control the information
that an agent believes.  However, once you have identified a belief set,
then I don't see any more problems with iff definitions that are already
present with if definitions.

peter
```
Received on Sunday, 26 November 2000 14:24:52 GMT

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