Pierre-louis Curien
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Introduction to linear logic and ludics, part I
2005, HAL (Le Centre pour la Communication Scientifique Directe)
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Abstract
In this two-part survey paper, we introduce linear logic and ludics, which were both introduced by Girard, in 1986 and 2001, respectively. They offer a thorough revisitation of mathematical logic from first principles, with inspiration from and applications to computer science. Some important keywords are: resources, geometry of computation, polarities, interaction, and games. We assume some basic knowledge of sequent calculus and natural deduction (see ), of λ-calculus (the classical reference is , see also ), and of category theory (only in section 7, see ). This paper is not trying to survey the whole and impressive body of works on linear logic since 17 years, but rather chooses a route that tries to highlight the deep originality of the subject. The bibliography is in consequence very partial (also reading the latter as a French word, wich meanss something like "personal", possibly biased). In sequent calculus, depending on presentations, you can see the left and right rules for, say, conjunction given
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