线性逻辑和态极逻辑引论(Ⅰ)

摘要

<线性逻辑和态极逻辑引论>一文概述了由Girard分别于1986和2001所创建的线性逻辑和态极逻辑.线性逻辑和态极逻辑汲取于计算机科学并反之应用于其中,从根本上对数理逻辑进行了彻底的审视.全文分为两部分.本文是文章的第一部分,致力于线性逻辑的联结词、证明规则、可判定性性质和模型.文章的第二部分将研究证明网并简要介绍态极逻辑.证明网是证明的图式表示,是线性逻辑的主要创新之一.%This two-parts paper offers a survey of linear logic and ludics, which were introduced by Girard in 1986 and 2001, respectively. Both theories revisit mathematical logic from first principles, with inspiration from and applications to computer science. The present part Ⅰ covers an introduction to the connectives and proof rules of linear logic, to its decidability properties, and to its models. Part Ⅱ will deal with proof nets, a graph-like representation of proofs which is one of the major innovations of linear logic, and will present an introduction to ludics.