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Re: Identity implies logic

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Thu, 27 Sep 2001 22:40:21 -0500
Message-Id: <p0510101cb7d99e06401a@[205.160.76.184]>
To: "Seth Russell" <seth@robustai.net>
Cc: www-rdf-logic@w3.org
>It seems to me that if the law of identity does not hold in a context, 

What law of identity are you referring to, exactly?

>then the Law of the Excluded Middle (LEM) and the Law of Non 
>Contradiction (LNC) are irrelevant and cannot be used in that 
>context. 

Why? I don't see the connection. (Presume you mean
LEM = P or (not P)
LNC = not (P and (not P))
right? These amount to the same thing in classical logic.)

>  For example:  If we have two different computers hooked up to the 
>semantic web and in one's database an apple is only known as 'apple' 
>and the other it is only known as 'orange',

Wait. How could you know that? That is, A is talking about things 
called A#apple, and B is talking about things called B#orange. How 
could you (or anyone) know they are supposed to be the same things?

>  then logical consequences that are inferred from the combination of 
>those two databases in that regard might  be erroneous. 

If you only make valid inferences, they will never be erroneous 
(unless you make them from erroneous premises, of course, but the 
logic can't check that for you.)  However, in general, one might be 
able to infer something from (A and B) that cannot be inferred from 
either A or B alone, so combining information from disparate sources 
is a risky business. It also suggests opportunities, though. ( Rather 
like life, right?)

However, I can't quite see how one could get errors from your 
example. The problem seems more to be the other way round: If A says 
A#apples are red, you ought to be able to infer that B#oranges are 
red too, but you can't. Your inferential abilities are too weak, not 
too strong.


>   In KIF I think this would be expressed something like:
>
>   (=> 
>       (holdsIn contextX IDENTITY)
>       (and
>           (holdsIn contextX LNC)
>           (holdsIn contextX LEM)
>   )
>

Not sure what that is supposed to mean.

>I have expressed this in the following mentograph:
><http://robustai.net/mentography/lawsOfLogic.gif>http://robustai.net/mentography/lawsOfLogic.gif
>
>Don't you think that a model theory for RDF should take this basic 
>assumption about when to apply strong logic into consideration?
>

The model theory just says how RDF graphs can be interpreted, and 
thereby how to infer valid conclusions. Not sure what you mean by 
strong logic, but validity of entailment *always* applies.

Pat Hayes
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Received on Thursday, 27 September 2001 23:40:26 UTC

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