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A system of interaction and structure
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2004
"... This paper introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative selfdual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, call ..."
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Cited by 113 (19 self)
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This paper introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative selfdual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae subject to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new topdown symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allowing the design of BV, yield a modular proof of cut elimination.
Noncommutative logic II: sequent calculus and phase semantics
, 1998
"... INTRODUCTION Noncommutative logic is a unication of :  commutative linear logic (Girard 1987) and  cyclic linear logic (Girard 1989; Yetter 1990), a classical conservative extension of the Lambek calculus (Lambek 1958). In a previous paper with Abrusci (Abrusci and Ruet 1999) we presented the mu ..."
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Cited by 27 (6 self)
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INTRODUCTION Noncommutative logic is a unication of :  commutative linear logic (Girard 1987) and  cyclic linear logic (Girard 1989; Yetter 1990), a classical conservative extension of the Lambek calculus (Lambek 1958). In a previous paper with Abrusci (Abrusci and Ruet 1999) we presented the multiplicative fragment of noncommutative logic, with proof nets and a sequent calculus based on the structure of order varieties, and a sequentialization theorem. Here we consider full propositional noncommutative logic. Noncommutative logic. Let us rst review the basic ideas. Consider the purely noncommutative fragment of linear logic, obtained by removing the exchange rule entirely : ` ; ; ; , ` ; ; ; y This work has been partly carried out at LIENSCNRS, Ecole Normale Superieure (Paris), at McGill University
Pomset logic as a calculus of directed cographs
 DYNAMIC PERSPECTIVES IN LOGIC AND LINGUISTICS
, 1999
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A Calculus of Order and Interaction
, 1999
"... System MV is a simple, propositional linear calculus that deals with the commutative as wel l as the noncommutative composition of structures. The mul tipl icative fragment of l near l gic is a special case of MV , and the tensor rul does not su#er from unnecessary nondeterminism in cont ..."
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Cited by 8 (1 self)
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System MV is a simple, propositional linear calculus that deals with the commutative as wel l as the noncommutative composition of structures. The mul tipl icative fragment of l near l gic is a special case of MV , and the tensor rul does not su#er from unnecessary nondeterminism in context partitioning as it does in the sequent calEE ofl ar l gic.
A λCalculus for Resource Separation
 In Automata, Languages and Programming: 31st International Colloquium, ICALP 2004, volume 3142 of LNCS
, 2004
"... Abstract. We present a typed λcalculus for recording resource separation constraints between terms. The calculus contains a novel way of manipulating nested multiplace contexts augmented with constraints, allowing a concise presentation of the typing rules. It is an extension of the affine αλcalc ..."
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Cited by 6 (0 self)
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Abstract. We present a typed λcalculus for recording resource separation constraints between terms. The calculus contains a novel way of manipulating nested multiplace contexts augmented with constraints, allowing a concise presentation of the typing rules. It is an extension of the affine αλcalculus. We give a semantics based on sets indexed by resources, and show how the calculus may be extended to handle nonsymmetric relations with application to allowable information flow. Finally, we mention some future directions and questions we have about the calculus. 1
A description of the nonsequential execution of Petrinets in partially commutative linear logic
, 2000
"... We encode the execution of Petri nets in Partially Commutative Linear Logic, an intuitionistic logic introduced by Ph. de Groote which contains both commutative and non commutative connectives. We are thus able to faithfully represent the concurrent firing of Petri nets as long as it can be depicted ..."
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Cited by 6 (4 self)
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We encode the execution of Petri nets in Partially Commutative Linear Logic, an intuitionistic logic introduced by Ph. de Groote which contains both commutative and non commutative connectives. We are thus able to faithfully represent the concurrent firing of Petri nets as long as it can be depicted by a seriesparallel order. This coding is inspired from the description of contextfree languages by Lambek grammars.
C.: Natural deduction and normalisation for partially commutative linear logic and lambek calculus with product
 Computation and Logic in the Real World, CiE
, 2007
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Handsome NonCommutative ProofNets: perfect matchings, seriesparallel orders and Hamiltonian circuits
 INRIA
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Provenance for Nondeterministic OrderAware Queries
"... Data transformations that involve (partial) ordering, and consolidate data in presence of uncertainty, are common in the context of various applications. The complexity of such transformations, in addition to the possible presence of metadata, call for provenance support. We introduce, for the fi ..."
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Cited by 2 (2 self)
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Data transformations that involve (partial) ordering, and consolidate data in presence of uncertainty, are common in the context of various applications. The complexity of such transformations, in addition to the possible presence of metadata, call for provenance support. We introduce, for the first time, a framework that accounts for the conjunction of these needs. To this end, we enrich the positive relational algebra with orderaware operators, some of which are nondeterministic, accounting for uncertainty. We study the expressive power and the complexity of deciding possibility for the obtained language. We then equip the language with (semiringbased) provenance tracking and highlight the unique challenges in supporting provenance for the orderaware operations. We explain how to overcome these challenges, designing a new provenance structure and a provenanceaware semantics for our language. We show the usefulness of the construction, proving that it satisfies common desiderata for provenance tracking. 1.
Author manuscript, published in "Computation and Logic in the Real World (Computing in Europe 2007), Siena: Italy (2007)" Natural Deduction and Normalisation for Partially Commutative Linear Logic and Lambek Calculus with Product
, 2009
"... Abstract. This paper provides a natural deduction system for Partially Commutative Intuitionistic Multiplicative Linear Logic (PCIMLL) and establishes its normalisation and subformula property. Such a system involves both commutative and non commutative connectives and deals with context that are se ..."
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Abstract. This paper provides a natural deduction system for Partially Commutative Intuitionistic Multiplicative Linear Logic (PCIMLL) and establishes its normalisation and subformula property. Such a system involves both commutative and non commutative connectives and deals with context that are seriesparallel multisets of formulæ. This calculus is the extension of the one introduced by de Groote presented by the second order for modelling Petri net execution, with a full entropy which allow order to be relaxed into any suborder — as opposed to the Non Commutative Logic of Abrusci and Ruet. Our result also includes, as a special case, the normalisation of natural deduction the Lambek calculus with product, which is unsurprising but yet unproved. Up to now PCIMLL with full entropy had no natural deduction. In particular for linguistic applications, such a syntax is much welcome to construct semantic representations from syntactic analyses. 1