Results 271 to 280 of about 3,702,791 (303)

The linear logic of multisets

Logic Journal of IGPL, 1998
The restricted use of weakening and contraction rules makes provability in Linear Logic (LL) sensitive to the number of occurrences of a formula in a sequent (one often says that LL is ``resource sensitive''). This suggests to look for a semantics of formulas for LL making use of the notion of multiset: a multiset over a set \(A\) is a function from ...
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A new deconstructive logic: linear logic

Journal of Symbolic Logic, 1997
AbstractThe main concern of this paper is the design of a noetherian and confluent normalization for LK2 (that is, classical second order predicate logic presented as a sequent calculus).The method we present is powerful: since it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's λμ, FD ([10, 12, 32, 36]),
Vincent Danos, Jean-Baptiste Joinet, Harold Schellinx   +2 more
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A “linear logic” Quicksort

ACM SIGPLAN Notices, 1994
The linear style of programming inspired by linear logic has been proposed to reduce garbage collection and synchronization costs in serial and parallel systems. We programmed Quicksort for both lists and arrays in a "linear" fragment of Lisp to estimate the performance impact of linearity on
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Linear logic and parallelism

1987
the paper discusses the relevance of a new logic called linear logic (Girard 1986) to computer science, and in particular to parallel computations. These general remarks will be detailed in a paper in preparation with Gianfranco Mascari.
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A syntax for linear logic

1994
There is a standard syntax for Girard's linear logic, due to Abramsky, and a standard semantics, due to Seely. Alas, the former is incoherent with the latter: different derivations of the same syntax may be assigned different semantics. This paper reviews the standard syntax and semantics, and discusses the problem that arises and a standard approach ...
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A taste of linear logic

1993
This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types”. The presentation of linear logic is simplified by basing it on the Logic of Unity. An application to the array update problem is briefly discussed.
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Logic Programming with Focusing Proofs in Linear Logic

Journal of Logic and Computation, 1992
Summary: The deep symmetry of linear logic makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and nonsymmetrical. I propose here one such model, in the area of logic programming, where the basic computational principle is: \[ \text{Computation}=\text{Proof search}.
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Linear logic as logic programming: An abstract

1997
Dans la lignee de ses travaux concernant la programmation logique, l'A. montre ici que la totalite de la logique lineaire peut etre consideree comme un langage de programmation logique qui permet une programmation de haut niveau et des primitives concurrents.
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Linear Logic and Intuitionistic Logic

Revue internationale de philosophie, 2004
Dans cet article je presente les fondements de la logique intuitioniste basee sur la logique lineair. Traditionnellement, la logique intuitioniste est concideree comme etant en disaccord avec les lois fondamentales de la logique classique sur la dualite, comme le tiers-exclu, les lois de Morgan, l'elimination de la double negation, etc.
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Quantum logic and linear logic

International Journal of Theoretical Physics, 1994
By tradition, the subject of quantum logic is the lattices of closed subspaces of Hilbert spaces or, more abstractly, orthomodular lattices. \textit{D. J. Foulis} showed in Can. J. Math. 17, 40-51 (1965; Zbl 0146.029) that an orthomodular lattice can be coordinatized by a Baer \(*\)- semigroup. On the other hand, \textit{C. J. Mulvey} [Rend. Circ. Math.
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