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A question about perspective

Date: Tue, 04 Feb 92 22:48:01 -0500
To: linear@cs.stanford.edu

I have a vague question about linear logic, so this seems like a
reasonable place to ask it.

First, I have to apologize.  I am a grandstudent of Tarski. I grew up
believing that semantics comes first, proof theory afterwards.  If my
career has been devoted to anything, it is to that belief. My current
work, on semantic theories of information, is still in that direction.
Trying to give an information-theoretic (in the semantic sense of
information) foundation to logic and inference. 

So while I love the elegance of Gentzen systems, and did some work in
them years ago, I genuinely have trouble understanding systems that
are not given an intuitively meaningful semantics, whether formal or
not, to motivate the rules of the system.

I am not being sarcastic when I phrase this as an apology.  I can tell
that something exciting is going on in linear logic.  All the signs
are there.  But I can't understand the system, at least not from what
I have seen.  (I've heard that Girard has a nice introduction, but in
French.)  I think i understand the intuitive meaning of "!" but not
some of the other connectives, which seem to be introduced for
proof-theoretic reasons.

So here is my question: how are you all thinking of these connectives?
Is there an intuitive semantics that motivates you, or are you
thinking about this system in a different way?  And if the latter, can
you explain the perspective to me?

Here is a possible response.  The different connectives represent
different ways of combining or processing information.  If that is the
line, then can one say more about the intuitive understanding of these
ways of combining information?  But maybe that is not the line at all.
Anyway, has anyone written something that answers these questions for
the likes of me?

I ask this for a self-interested reason. Lately in my work on
information links, I have been seeing tell-tale hints of connections
between it and relevance and linear logic.  But the parallels are all
at a formal level.  I suspect that there must be deeper affinities,
that there must be something basically semantic behind the systems.  I
would like to come to understand what it is.

Thanks in advance for any help.  

Jon Barwise

p.s. I am aware of the coherence space semantics and the phase space
semantics. But they don't satisfy my quest for an intuitive semantics
that motivates the rules.  Maybe there is another out there that will.