By Jean-Yves Girard, Yves Lafont, Laurent Regnier

ISBN-10: 0521559618

ISBN-13: 9780521559614

This quantity offers an summary of linear good judgment in 5 components: classification thought; complexity and expressivity; facts thought; facts nets; and the geometry of interplay. The e-book encompasses a basic advent to linear common sense that may verify this book's use via the beginner in addition to the specialist. Mathematicians and desktop scientists will research a lot from this publication.

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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. Marcel Dekker. -Y. Girard, Y. Lafont, and P. Taylor. Proofs and types, volume 7 of Cambridge tracts in theoretical computer science. Cambridge University Press, 1990.

This can easily be extended to yield an interpretation of quantifiers (intersection and biorthogonal of the union). Observe that the definitions satisfy the obvious De Morgan laws relating ® and ' etc. A non-trivial exercise is to prove the associativity of 0. 3 Soundness and completeness It is easily seen that the semantics is sound and complete : Theorem 2 A formula A of linear logic is provable if for any interpretation (involving a phase space (M, 1)), the interpretation At of A contains the neutral element 1.

Lambek. Bilinear logic in algebra and linguistics. In this volume, 1995. [24] P. Lincoln. 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.

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