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From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math,sci.logic,comp.theory
Subject: Re: Linear Logic
Summary: Why linear logic generally does not work
Keywords: Linear Logic
Message-ID: <12621@mentor.cc.purdue.edu>
Date: 22 May 91 14:05:16 GMT
Article-I.D.: mentor.12621
References: <3023@puck.sw.mcc.com> <1991May16.232218.8032@newshost.anu.edu.au> <1991May21.222324.12820@cs.ubc.ca>
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There have been attempts to come up with a reasonable linear logic since at
least 1919.  The problem is that they run into extreme difficulties.

A simple example is the truth value of X&Y, where that of X is .5, as is
that of Y.  Now what if Y is X?  What if Y is ~X?  The extension needed
to take care of things like this is probability.

Linear logics are possible in "Brouwerian" logic, but unless X is false,
~X is false.  Negations in Brouwerian logic satisfy Boolean logic.

Certainly one can define any type of system one wants, but giving it a
catchy name like linear logic or fuzzy logic does not mean that is succeeds
in accomplishing its ostensible purpose.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet)   {purdue,pur-ee}!l.cc!hrubin(UUCP)