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Re: Linear notation
Date: Sun, 29 Dec 91 12:43:51+020
To: linear@cs.stanford.edu
Since there were so many messages about notations, I feel that I should do
some justice to the relevantist's notation, if only on the ground of priority.
J.Y. has admitted himself that relevance logicans were the first to
distinguish between the "multiplicative" and "additive" conjunction and
disjunction (called by them intensional and extensional, respectively).
They have of course their own notation for them, which is well established
in several books and plenty of papers and was used for more than twenty
years before Linear Logic was born. I think that simply ignoring this is
not ethical. Worse: if people use + (the relevantists notation for "par")
for the additive disjunction then a lot of confusion can arise, and I like
to believe that nobody wants it.
Except for the issue of priority, I believe that the simple models of
Linear logic in the integers and in the reals which were used lately
by several authors (including myself) and in which "par" is interpreted as
the usual addition of numbers (+) vindicate the relevantists intuition in
their choice of notation.
Arnon Avron