Introduction to linear logic

is manuscript is the lecture notes for the course of the same title I gave at the Summer school on linear logic and geometry of interaction that took place in Torino in August 2013. e aim of this course is to give a broad introduction to linear logic, covering enough ground to present many of the ideas and techniques of the field, while staying at a (hopefully) accessible level for beginners. For this reason, most technical development is carried out in the simple multiplicative fragment, with only hints at generaliza- tions. As prerequisites, some knowledge of classical sequent calculus and some knowledge of the �� -calculus is useful.

[1]  Vincent Danos,et al.  The structure of multiplicatives , 1989, Arch. Math. Log..

[2]  J. Girard,et al.  Proofs and types , 1989 .

[3]  Jean-Yves Girard,et al.  A new constructive logic: classic logic , 1991, Mathematical Structures in Computer Science.

[4]  Jean-Yves Girard,et al.  Linear logic: its syntax and semantics , 1995 .

[5]  Natarajan Shankar,et al.  Decision problems for propositional linear logic , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[6]  Patrick Lincoln,et al.  Linear logic , 1992, SIGA.

[7]  Rob J. van Glabbeek,et al.  Proof nets for unit-free multiplicative-additive linear logic , 2005, TOCL.

[8]  Vincent Danos,et al.  A new deconstructive logic: linear logic , 1997, Journal of Symbolic Logic.

[9]  Jean-Marc Andreoli Proposition pour une synthese des paradigmes de la programmation logique et de la programmation par objets , 1990 .