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Re: T&A Boxes (was: RE: rdf as a base for other languages)

From: pat hayes <phayes@ai.uwf.edu>
Date: Thu, 14 Jun 2001 14:53:55 -0500
Message-Id: <v04210102b74ec51c13cc@[205.160.76.189]>
To: Drew McDermott <drew.mcdermott@yale.edu>
Cc: www-rdf-logic@w3.org
>   [Pat Hayes]
>   As far as I know, there is no *mathematical* way to distinguish
>   definitions and assertions.
>
>Correct me if I'm wrong, but don't logic textbook mention the case
>where a definition is simply an equality or if-and-only-if?  E.g., you
>might write (bachelor ?x) <=> (and (male ?x) (not (married ?x))).  Now
>take a theory involving the term "bachelor," and you can easily
>convert it to a theory that doesn't mention the term anywhere.  This
>two-stage process neatly captures the idea of the definition "not
>being allowed to be false."  By the time you catch a contradiction,
>the definition is nowhere to be seen.

Well, yes, that two-stage process does kind of ensure that the stuff 
eliminated in the first stage can't be changed (since it isnt around 
any more). But so what? Once you remove the biconditional, you have a 
*different* set of sentences, and it doesn't have the same 
consequences (eg you can't infer from it that anything is a 
bachelor).  And in any case, that trick applies to any kind of 
expression, not just IFF s and equalities. Eg take a set of clauses, 
choose one of them that isnt self-resolving, resolve it with all the 
others in every possible way, then erase it. Now you have a set of 
clauses from which the orginal clause can't be 'removed'. So almost 
any clause can be a definition in this sense.

>Of course, this won't work for recursive definitions, which may be why
>people like Russell didn't trust them.  My knowledge of the history of
>logic is a bit shaky at this point.

There are deeper reasons to be mistrustful of recursive definitions, 
or at least there were before fixed-point semantics was invented.

Pat

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Received on Thursday, 14 June 2001 15:53:49 GMT

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