[sci.logic] some references to linear logic

paul@laas.fr (Paul Freedman) (05/17/91)

last december, "oscar@cuisun.unige.ch" 
sent me a summary of references to linear logic which he had received
from dwight spencer (dwights@cse.ogi.edu)

girard is not easy to read, neither in English nor in French,
and that's why it's wiser to read what other people have written 
about his work first.
i trust that i won't be offending anyone if i simply post
that message to the net.

but first, let me add my two cents.

- if your reading French is pretty good, then you might
try Girard's introductory article which appeared in the 
journal "Science et la Vie", the French version of "Scientific American",
in the april 1990 issue.
there are some inconsistencies in the article, but the examples are fun.

- if you're interested in links to planning (in the AI sense), you might
want to ask for the following technical report (written in English)
from a group working at the University of Paris-Nord:

"Generating Plans in Linear Logic", 
M. Masseron, C. Tollu, J. Vauzeilles, 
no. 90-11 December 1990
best to write to Vauzeilles, care of
	Universite' Paris-Nord
	De'partement de mathe'matiques et informatique
	93430 Villetaneuse
	France

- Here at LAAS, some people are looking at links to petri net theory, 
re-formulating some of Girard's connectives in PN terms.
the best person to contact is Robert Valette
(robert@laas.fr) for details

paul freedman
(paul@laas.fr)


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From:    Dwight Spencer 
To:      <oscar@cui.unige.ch>
Subject: Re: Wanted: Intro to Linear Logic

The first two below are all-important. The third (by Girard) has a lot of good
intuition about linear logic. The others have nice introductions embedded
within them.

  A Brief Guide to Linear Logic
  A. Scedrov
  Bulletin of the EATCS 41, June 1990, pg. 154-165

[to my mind, this article by scedrov is by far the best place to start .. paul]

  Introduction to Linear Logic
  Y. Lafont
  Lecture Notes for Summer School on Constructive Logics and
    Category Theory (Isle of Thorns, August 1988)

  Towards A Geometry of Interaction
  J-Y. Girard
  Contemporary Mathematics 92, 1989, pg. 69-108
  
  The Linear Abstract Machine
  Y.Lafont
  Theoretical Computer Science 59 (1988), pg. 157-180

  From Petri Nets to Linear Logic
  N. Mart\'{i}-Oliet and J. Meseguer
  CSLI Tech Report

  Petri Nets as Models of Linear Logic
  U. Engberg and G. Winskel
  CAAP '90, LNCS 431, pg. 147-161

  Relating Petri Nets to Formulas of Linear Logic
  C. Brown
  Edinburgh Tech. Report ECS-LFCS-89-87 (June, 1989)

  An Algebraic Axiomization of Linear Logic Models
  N. Mart\'{i}-Oliet and J. Meseguer
  CSLI Tech Report

  Linear Logic and Lazy Computation
  J-Y. Girard
  TAPSOFT 1987, LNCS 250, pg. 52-66

  Computational Interpretations of Linear Logic
  S. Abramsky
  Imperial College Research Report DOC 90/20 (Oct. 1990)

And then there's the categorical models, but I'll just cite the probable
starting point for the categorically-aware:
  
  Linear Logic, *-autonomous Categories and Cofree Coalgebras
  R. A. G. Seely
  Contemporary Mathematics 92, 1989, pg. 371-382

Enjoy!


- Dwight Spencer              dwights@cse.ogi.edu

  Dept. of Computer Science and Engineering
  Oregon Graduate Institute
  19600 N. W. Von Neumann Drive
  Beaverton, Oregon
  97006-1999
  USA

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