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Relations and Noncommutative Linear Logic
, 1991
"... Linear logic [Gir87, GL87] differs from intuitionistic logic primarily in the absence of the structural rules of weakening and contraction. Weakening allows us to prove a proposition in the context of irrelevant or unused premises, while contraption allows us to use a premise an arbitrary number of ..."
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Cited by 15 (0 self)
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Linear logic [Gir87, GL87] differs from intuitionistic logic primarily in the absence of the structural rules of weakening and contraction. Weakening allows us to prove a proposition in the context of irrelevant or unused premises, while contraption allows us to use a premise an arbitrary number
Natural Deduction for Intuitionistic NonCommutative Linear Logic
 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications (TLCA'99
, 1999
"... We present a system of natural deduction and associated term calculus for intuitionistic noncommutative linear logic (INCLL) as a conservative extension of intuitionistic linear logic. We prove subject reduction and the existence of canonical forms in the implicational fragment. ..."
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Cited by 36 (16 self)
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We present a system of natural deduction and associated term calculus for intuitionistic noncommutative linear logic (INCLL) as a conservative extension of intuitionistic linear logic. We prove subject reduction and the existence of canonical forms in the implicational fragment.
Focusing and ProofNets in Linear and NonCommutative Logic
 Proceedings of 6th International Conference on Logic Programming and Automated Reasoning
, 1999
"... Linear Logic [4] has raised a lot of interest in computer research, especially because of its resource sensitive nature. One line of research studies proof construction procedures and their interpretation as computational models, in the "Logic Programming" tradition. An efficient proof s ..."
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Cited by 16 (2 self)
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. This is, in particular, the case of the NonCommutative logic of [1], and all the computational exploitation of Focusing which has been performed in the commutative case can thus be revised and adapted to the non commutative case.
Noncommutativity and MELL in the Calculus of Structures
 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2001
"... We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a selfdual noncommutative operator inspired by CCS, that seems not to be expressible in ..."
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Cited by 61 (24 self)
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We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a selfdual noncommutative operator inspired by CCS, that seems not to be expressible
Algorithmic specifications in linear logic with subexponentials
 In ACM SIGPLAN Conference on Principles and Practice of Declarative Programming (PPDP
, 2009
"... nigam at lix.polytechnique.fr, dale.miller at inria.fr The linear logic exponentials!, ? are not canonical: one can add to linear logic other such operators, say! l, ? l, which may or may not allow contraction and weakening, and where l is from some preordered set of labels. We shall call these add ..."
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Cited by 19 (9 self)
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these additional operators subexponentials and use them to assign locations to multisets of formulas within a linear logic programming setting. Treating locations as subexponentials greatly increases the algorithmic expressiveness of logic. To illustrate this new expressiveness, we show that focused proof search
Pomset Logic: A NonCommutative Extension of Classical Linear Logic
, 1997
"... We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherenc ..."
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Cited by 41 (10 self)
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We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine
Noncommutative logic I : the multiplicative fragment
, 1998
"... INTRODUCTION Unrestricted exchange rules of Girard's linear logic [8] force the commutativity of the multiplicative connectives\Omega (times, conjunction) and & (par, disjunction) , and henceforth the commutativity of all logic. This a priori commutativity is not always desirable  it is ..."
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Cited by 41 (7 self)
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 it is quite problematic in applications like linguistics or computer science , and actually the desire of a noncommutative logic goes back to the very beginning of LL [9]. Previous works on noncommutativity deal essentially with noncommutative fragments of LL, obtained by removing the exchange rule
A NonCommutative Extension of MELL
, 2002
"... We extend multiplicative exponential linear logic (MELL) by a noncommutative, selfdual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We ..."
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Cited by 30 (12 self)
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We extend multiplicative exponential linear logic (MELL) by a noncommutative, selfdual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We
Relating Natural Deduction and Sequent Calculus for Intuitionistic NonCommutative Linear Logic
, 1999
"... We present a sequent calculus for intuitionistic noncommutative linear logic (INCLL) , show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cutfree derivations, and arbitrary natura ..."
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Cited by 29 (16 self)
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We present a sequent calculus for intuitionistic noncommutative linear logic (INCLL) , show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cutfree derivations, and arbitrary
Noncommutative logic III: focusing proofs
 Information and Computation
, 2000
"... We present a sequent calculus for noncommutative logic which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying the permut ..."
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Cited by 5 (2 self)
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and the second author in [1, 15] (see also section 3). It unies commutative linear logic [6] and cyclic linear logic [16], a classical conservative extension of the Lambek calculus [10]. The present paper investigates the \focalization" property for noncommutative logic. 1.1 The property of focalization
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