Re: Grist for layering discussion

I have been guilty of misrepresenting the law of the excluded middle.

The Law of the Excluded Middle states that any proposition is either true
or false, i.e., no other possibilities exist.  There are several logical
systems that do not have the Law of the Excluded Middle.  These logics, in
essense, add one, or more, other possible situations for a proposition.
Some such logics add an ``undefined''; some add a ``contradictory''; some
add both; some add even more.  Some logics even abandon the whole idea of
propositions have a truth value.

From: Peter F. Patel-Schneider <>
Subject: Re: Grist for layering discussion 
Date: Fri, 11 Jan 2002 20:14:08 -0500

> > The normal way you do it relies on the Princple of the Excluded middle,
> > which of course cannot be part of the semantic web.
> Why not?  Well, of course, I don't want to deduce anything just because
> some web page says X and some other web page says not X, but there are lots of
> formalisms that don't have this property and that have the Law of the
> Excluded Middle.

I should have gone on and said:

There are logics (including most of the first group above) that don't have
the Law of the Excluded Middle but nonetheless would be able to deduce
anything from an explicit contradiction.  There are other logics (including
most of the second group above) where even explicit contradictions don't
enable the inference of all propositions.

You can't claim that abandoning the Law of the Excluded Middle solves a
particular problem without saying what you are going to replace it by.

Peter F. Patel-Schneider
Bell Labs Research

Received on Saturday, 12 January 2002 10:18:10 UTC