Showing papers by "Jean-Yves Girard published in 1993"

Linear Logic: A Survey

Abstract: This introduction to linear logic is organised in four chapters: 1. Thesyntaxof linearlogic Here the formal system is introduced, with a special emphasis on the treatment of structural rules: weakening and contraction become logical rules for new connectives, 7 and !. Informal examples are introduced to illustrate this shift of viewpoint: linear logic is not about situations but about actions. 2. Thedenotational semantics of linear logic Coherent spaces (a drastic simplification of Scott domains) are introduced; semantically speaking, linear logic appears as a refinement of intuitionistic logic. 3. Proof-nets The specificities of linear logic (e.g., symmetries I/O) suggest a new kind of syntax for proofs, with intrinsic parallel features. Proof-nets are graphs (and not trees as usual) without explicit sequentialization; the difficult question is precisely that of the correcmess criterion, i.e., of the existence of implicit sequentialisations. 4. On the unity of logic This chapter is about logic (without adjective): from the experience gathered in linear logic, it seems possible to put all (decent) logical systems together. A sequent calculus LU is introduced: classical, intuitionistic and linear logics appear as fragments of this unified system. Many aspects of linear logic (especially applied ones) have been excluded from this approach; not because they are inessential, but because they do not fit with our pattern. We shall not try to make an enumeration (necessarily superficial) of these missing topics. Maybe the approach to linear logic though other authors (especially [Sv] and [T] which contain good bibliographies) is the best way to complete this initiation.