Results 1 
4 of
4
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 90 (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...
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.
Sequentiality vs. Concurrency in Games and Logic
 Math. Structures Comput. Sci
, 2001
"... Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic. ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.
A denotational semantics for the symmetric interaction combinators
 Mathematical Structures in Computer Science
, 2007
"... The symmetric interaction combinators are a variant of Lafont’s interaction combinators. They enjoy a weaker universality property with respect to interaction nets, but are equally expressive. They are a model of deterministic distributed computation, sharing the good properties of Turing machines ( ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
The symmetric interaction combinators are a variant of Lafont’s interaction combinators. They enjoy a weaker universality property with respect to interaction nets, but are equally expressive. They are a model of deterministic distributed computation, sharing the good properties of Turing machines (elementary reductions) and of the λcalculus (higherorder functions, parallel execution). We introduce a denotational semantics for this system, inspired by the relational semantics for linear logic, proving an injectivity and full completeness result for it. We also consider the algebraic semantics defined by Lafont, and prove that the two are strongly related. 1