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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 37 (8 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 coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly we extend the syntax of multiplicative proof nets to these new operations. We then prove strong normalisation, and confluence. Coming back to the denotational semantics that we started with, we establish in an unusual way the soundness of this calculus with respect to the semantics. The converse, i.e. a kind of completeness result, is simply stated: we refer to a report for its lengthy proof. We conclude by mentioning more results, including a sequent calculus which is interpreted by both the semantics and the proof net syntax, although we are not sure that it takes all proof nets into account...
A Purely Logical Account of Sequentiality in Proof Search
, 2002
"... A strict correspondence between the proofsearch space of a logical formal system and computations in a simple process algebra is established. Sewuential ..."
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Cited by 24 (3 self)
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A strict correspondence between the proofsearch space of a logical formal system and computations in a simple process algebra is established. Sewuential
Pomset Logic as an Alternative Categorial Grammar
 IN FORMAL GRAMMAR
, 1995
"... Lambek calculus may be viewed as a fragment of linear logic, namely intuitionistic noncommutative multiplicative linear logic. As it is too restrictive to describe numerous usual linguistic phenomena, instead of extending it we extend MLL with a noncommutative connective, thus dealing with partia ..."
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Cited by 17 (2 self)
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Lambek calculus may be viewed as a fragment of linear logic, namely intuitionistic noncommutative multiplicative linear logic. As it is too restrictive to describe numerous usual linguistic phenomena, instead of extending it we extend MLL with a noncommutative connective, thus dealing with partially ordered multisets of formulae. Relying on proof net technique, our study associates words with parts of proofs, modules, and parsing is described as proving by plugging modules. Apart from avoiding spurious ambiguities, our method succeeds in obtaining a logical description of relatively free word order, headwrapping, clitics, and extraposition (these latest two constructions are unfortunately not included, for lack of space).
Pomset logic as a calculus of directed cographs
 DYNAMIC PERSPECTIVES IN LOGIC AND LINGUISTICS
, 1999
"... ..."
A Linear Logic View of Gamma Style Computations as Proof Searches
 Coordination Programming: Mechanisms, Models and Semantics. Imperial
"... Using the methodology of abstract logic programming in linear logic, we establish a correct and complete translation between the language Nabla and first order linear logic. Nabla is a modification of the coordination language Gamma with parallel and sequential composition. Nabla, without modifyin ..."
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Cited by 7 (0 self)
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Using the methodology of abstract logic programming in linear logic, we establish a correct and complete translation between the language Nabla and first order linear logic. Nabla is a modification of the coordination language Gamma with parallel and sequential composition. Nabla, without modifying Gamma basic computational model, is amenable to this kind of analysis, at the price of a weaker expressive power. The translation is correct and complete in the sense that we establish a two way correspondence between computations in Nabla and the search for proofs in a suitable fragment of first order linear logic. Moreover, the translation is not an encoding, meaning that to the algebraic structure of Nabla programs is assigned logical meaning through a nontrivial use of linear logic connectives, as opposed to merely reflecting their operational behavior through a simulation into terms of the logic. In this way we hope that the connection established between the two formalisms can compe...
Sequentiality by Linear Implication and Universal Quantification
 In Jorg Desel, editor, Structures in Concurrency Theory, Workshops in Computing
, 1995
"... In this paper we address the issue of understanding sequential and parallel composition of agents from a logical viewpoint. We use the methodology of abstract logic programming in linear logic, where computations are proof searches in a suitable fragment of linear logic. While parallel composition h ..."
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Cited by 6 (2 self)
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In this paper we address the issue of understanding sequential and parallel composition of agents from a logical viewpoint. We use the methodology of abstract logic programming in linear logic, where computations are proof searches in a suitable fragment of linear logic. While parallel composition has a straightforward treatment in this setting, sequential composition is much more difficult to be obtained. We define and study a logic programming language, SMR, in which the causality relation among agents forms a seriesparallel order; top agents are recursively rewritten by seriesparallel structures of new agents. We show a declarative and simple treatment of sequentialization, which smoothly integrates with parallelization, by translating SMR into linear logic in a complete way. This means that we obtain a full two ways correspondence between proofs in linear logic and computations in SMR; thus we have full correspondence between the two formalisms. Our case study is very general per ...
A Highly Parallel Model for ObjectOriented Concurrent Constraint Programming
 Proc. IEEE ICA PP95
, 1995
"... Two of the currently most promising programming paradigms, namely ObjectOriented Programming and Concurrent Constraint Programming are combined into a single, highly parallel computational model based on Term Graph Rewriting Systems. In particular, we show how multiheaded Term Graph rewrite rules ..."
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Cited by 4 (4 self)
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Two of the currently most promising programming paradigms, namely ObjectOriented Programming and Concurrent Constraint Programming are combined into a single, highly parallel computational model based on Term Graph Rewriting Systems. In particular, we show how multiheaded Term Graph rewrite rules provide a powerful tool able to manipulate Term Graphs which themselves represent in a homogeneous way objects, concurrently executing agents and constraints. Due to the inherent fine grain parallelism of Term Graph Rewriting the proposed model is highly parallel with all activities (object communication, agent execution and constraint solving) executing concurrently. 1. Introduction The generalised computational model of Term Graph Rewriting Systems (TGRS) ([5]) has been used extensively as an implementation vehicle for a number of, often divergent, programming paradigms ranging from the traditional functional programming ones ([12,15]) to the (concurrent) logic programming ones ([3,10,18])...
On Linear Logic Planning and Concurrency
"... We present an approach to linear logic planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. This is performed by extracting partial order plans from sound and complete encodings of planning problems in multiplicativ ..."
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Cited by 1 (1 self)
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We present an approach to linear logic planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. This is performed by extracting partial order plans from sound and complete encodings of planning problems in multiplicative exponential linear logic in a way that exhibits a noninterleaving behavioral concurrency semantics. Relying on this fact, we argue that this work is a crucial step for establishing a common language for concurrency and planning that will allow to carry techniques and methods between these two fields.