By Jean-Yves Girard, Yves Lafont, Laurent Regnier

ISBN-10: 0521559618

ISBN-13: 9780521559614

This quantity provides an outline of linear good judgment in 5 elements: type idea; complexity and expressivity; evidence conception; facts nets; and the geometry of interplay. The ebook features a normal advent to linear good judgment that may determine this book's use by way of the beginner in addition to the specialist. Mathematicians and machine scientists will study a lot from this e-book.

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Linear logic. Theoretical Computer Science, 50:1-102, 1987. -Y. Girard. A new constructive logic : classical logic. Mathematical structures in Computer Science, 1:255-296, 1991. -Y. Girard. On the unity of logic. Annals of Pure and Applied Logic, 59:201-217, 1993. -Y. Girard. Geometry of interaction III : accommodating the additives. In this volume, 1995. -Y. Girard. Light linear logic. in preparation, 1995. -Y. Girard. Proof-nets : the parallel syntax for proof-theory. In Logic and Algebra, New York, 1995.

The move to multisets is a consequence of recent progress on classical logic [12] for which this replacement has deep consequences. But as far as linear and intuitionistic logic are concerned, we can work with sets, and this is what will be assumed here. In particular M(X) will be replaced by the monoid of finite subsets of X, and sum will be replaced by union. X will be the set _Xfin of all finite cliques of X. if aeX then F(a) c: Y, 2. assume that a = U bi, where bi is directed with respect to inclusion, then F(a) = U F(bi), 3.

Deciding provability of linear logic fragments. In this volume, 1995. [25] P. C. C. Shankar, and A. Scedrov. Decision problems for propositional linear logic. In Proceedings of 31st IEEE symposium on foundations of computer science, volume 2, pages 662-671. IEEE Computer Society Press, 1990. [26] Laurent Regnier. Lambda-Calcul et Reseaux. These de doctorat, Universite Paris 7, 1992. N. Yetter. Quantales and non-commutative linear logic. Journal of Symbolic Logic, 55:41-64, 1990. Bilinear logic in algebra and linguistics o) J.

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