Results 1  10
of
180
Bigraphs and Mobile Processes
, 2003
"... A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and comm ..."
Abstract

Cited by 1064 (29 self)
 Add to MetaCart
A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In part I, we illustrate...
Logic Programming with Focusing Proofs in Linear Logic
 Journal of Logic and Computation
, 1992
"... The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is C ..."
Abstract

Cited by 344 (8 self)
 Add to MetaCart
The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is Computation = Proof search.
Games and Full Completeness for Multiplicative Linear Logic
 JOURNAL OF SYMBOLIC LOGIC
, 1994
"... We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the den ..."
Abstract

Cited by 215 (26 self)
 Add to MetaCart
We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cutfree proof net. A key role is played by the notion of historyfree strategy; strong connections are made between historyfree strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass et al.
The Geometry of Optimal Lambda Reduction
, 1992
"... Lamping discovered an optimal graphreduction implementation of the calculus. Simultaneously, Girard invented the geometry of interaction, a mathematical foundation for operational semantics. In this paper, we connect and explain the geometry of interaction and Lamping's graphs. The geometry o ..."
Abstract

Cited by 106 (2 self)
 Add to MetaCart
Lamping discovered an optimal graphreduction implementation of the calculus. Simultaneously, Girard invented the geometry of interaction, a mathematical foundation for operational semantics. In this paper, we connect and explain the geometry of interaction and Lamping's graphs. The geometry of interaction provides a suitable semantic basis for explaining and improving Lamping's system. On the other hand, graphs similar to Lamping's provide a concrete representation of the geometry of interaction. Together, they offer a new understanding of computation, as well as ideas for efficient and correct implementations.
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
Abstract

Cited by 96 (17 self)
 Add to MetaCart
Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
Bigraphs and Mobile Processes (revised)
, 2004
"... A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and comm ..."
Abstract

Cited by 62 (6 self)
 Add to MetaCart
A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In Part I we illustrate...
From ProofNets to Interaction Nets
 Advances in Linear Logic
, 1994
"... Introduction If we consider the interpretation of proofs as programs, say in intuitionistic logic, the question of equality between proofs becomes crucial: The syntax introduces meaningless distinctions whereas the (denotational) semantics makes excessive identifications. This question does not hav ..."
Abstract

Cited by 61 (1 self)
 Add to MetaCart
(Show Context)
Introduction If we consider the interpretation of proofs as programs, say in intuitionistic logic, the question of equality between proofs becomes crucial: The syntax introduces meaningless distinctions whereas the (denotational) semantics makes excessive identifications. This question does not have a simple answer in general, but it leads to the notion of proofnet, which is one of the main novelties of linear logic. This has been already explained in [Gir87] and [GLT89]. The notion of interaction net introduced in [Laf90] comes from an attempt to implement the reduction of these proofnets. It happens to be a simple model of parallel computation, and so it can be presented independently of linear logic, as in [Laf94]. However, we think that it is also useful to relate the exact origin of interaction nets, especially for readers with some knowledge in linear logic. We take this opportunity to give a survey of the theory of proofnets, including a new proof of the sequentializ
Linear Logic Without Boxes
, 1992
"... Girard's original definition of proof nets for linear logic involves boxes. The box is the unit for erasing and duplicating fragments of proof nets. It imposes synchronization, limits sharing, and impedes a completely local view of computation. Here we describe an implementation of proof nets w ..."
Abstract

Cited by 54 (0 self)
 Add to MetaCart
Girard's original definition of proof nets for linear logic involves boxes. The box is the unit for erasing and duplicating fragments of proof nets. It imposes synchronization, limits sharing, and impedes a completely local view of computation. Here we describe an implementation of proof nets without boxes. Proof nets are translated into graphs of the sort used in optimal calculus implementations; computation is performed by simple graph rewriting. This graph implementation helps in understanding optimal reductions in the calculus and in the various programming languages inspired by linear logic. 1 Beyond the calculus The calculus is not entirely explicit about the operations of erasing and duplicating arguments. These operations are important both in the theory of the  calculus and in its implementations, yet they are typically treated somewhat informally, implicitly. The proof nets of linear logic [1] provide a refinement of the calculus where these operations become explici...
A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
Abstract

Cited by 53 (8 self)
 Add to MetaCart
An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.