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System BV is NPcomplete
, 2005
"... System BV is an extension of multiplicative linear logic (MLL) with the rules mix, nullary mix, and a selfdual, noncommutative logical operator, called seq. While the rules mix and nullary mix extend the deductive system, the operator seq extends the language of MLL. Due to the operator seq, syste ..."
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Cited by 9 (4 self)
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System BV is an extension of multiplicative linear logic (MLL) with the rules mix, nullary mix, and a selfdual, noncommutative logical operator, called seq. While the rules mix and nullary mix extend the deductive system, the operator seq extends the language of MLL. Due to the operator seq, system BV extends the applications of MLL to those where sequential composition is crucial, e.g., concurrency theory. System FBV is an extension of MLL with the rules mix and nullary mix. In this paper, by relying on the fact that system BV is a conservative extension of system FBV, I show that system BV is NPcomplete by encoding the 3Partition problem in FBV. I provide a simple completeness proof of this encoding by resorting to a novel proof theoretical method for reducing the nondeterminism in proof search, which is also of independent interest.
Labelled Deduction
, 2000
"... In this paper, we propose new labelled proof systems to analyse the intuitionistic provability in classical and linear logics. An important point is to understand how search in a nonclassical logic can be viewed as a perturbation of search in classical logic. Therefore, suitable characterizations o ..."
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Cited by 6 (3 self)
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In this paper, we propose new labelled proof systems to analyse the intuitionistic provability in classical and linear logics. An important point is to understand how search in a nonclassical logic can be viewed as a perturbation of search in classical logic. Therefore, suitable characterizations of intuitionistic provability and related labelled sequent calculi are defined for linear logic. An alternative approach, based on the notion of proofnet and on the definition of suitable labelled classical proofnets, allows to directly study the intuitionistic provability by constructing intuitionistic proofnets for sequents of classical linear logic. Keywords: Proof theory, intuitionistic logic, linear logic, labelled sequent calculus, proofnets, automated deduction. 1. INTRODUCTION Many proofsearch methods (sequent calculus, tableaux, resolution, connections) have been naturally developed in classical logic (CL) with a view 1 2 LABELLED DEDUCTION to avoiding the possible redundanc...
A Formulation of Linear Logic Based on DependencyRelations
 In Proc. of Computer Science Logic '97, Lecture Notes in Computer Science
, 1997
"... In this paper we describe a solution to the problem of proving cutelimination for FILL, a variant of exponentialfree and multiplicative Linear Logic originally introduced by Hyland and de Paiva. In the work of Hyland and de Paiva, a term assignment system is used to describe the intuitionistic cha ..."
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Cited by 6 (3 self)
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In this paper we describe a solution to the problem of proving cutelimination for FILL, a variant of exponentialfree and multiplicative Linear Logic originally introduced by Hyland and de Paiva. In the work of Hyland and de Paiva, a term assignment system is used to describe the intuitionistic character of FILL and a proof of cutelimination is barely sketched. In the present paper, as well as correcting a small mistake in their work and extending the system to deal with exponentials, we introduce a different formal system describing the intuitionistic character of FILL and we provide a full proof of the cutelimination theorem. The formal system is based on a dependencyrelation between formulae occurrences within a given proof and seems of independent interest. The procedure for cutelimination applies to (multiplicative and exponential) Classical Linear Logic, and we can (with care) restrict our attention to the subsystem FILL. The proof, as usual with cutelimination proofs, is...
A Deductive Compositional Approach to Petri Nets for Systems Biology
"... We introduce the language CP, a compositional language for place transition petri nets for the purpose of modelling signalling pathways in complex biological systems. We give the operational semantics of the language CP by means of a proof theoretical deductive system which extends multiplicative e ..."
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Cited by 1 (1 self)
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We introduce the language CP, a compositional language for place transition petri nets for the purpose of modelling signalling pathways in complex biological systems. We give the operational semantics of the language CP by means of a proof theoretical deductive system which extends multiplicative exponential linear logic with a selfdual noncommutative logical operator. This allows to express parallel and sequential composition of processes at the same syntactic level as in process algebra, and perform logical reasoning on these processes. We demonstrate the use of the language on a model of a signaling pathway for Fc receptormediated phagocytosis.
Categorical Proof Theory of CoIntuitionistic Linear Logic
"... Summary. To provide a categorical semantics for cointuitionistic logic, one has to face the fact, noted by Tristan Crolard, that the definition of coexponents as adjuncts of coproducts does not work in the category Set, where coproducts are disjoint unions. Following the familiar construction of ..."
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Cited by 1 (1 self)
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Summary. To provide a categorical semantics for cointuitionistic logic, one has to face the fact, noted by Tristan Crolard, that the definition of coexponents as adjuncts of coproducts does not work in the category Set, where coproducts are disjoint unions. Following the familiar construction of models of intuitionistic linear logic with exponent!, we build models of cointuitionistic logic in symmetric monoidal closed categories with additional structure, using a variant of Crolard’s term assignment to cointuitionistic logic in the construction of a free category. 1
Proof Net Semantics of Proof Search Computation Lu'is Caires and Lu'is Monteiro
, 1997
"... Abstract. We present a sound and complete compositional semantics, structured around certain abstractions of proof nets, for proofsearch computation in a linear logicbased language. The model captures the interaction of agents in terms of the actions they engage into and of the dynamic creation of ..."
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Abstract. We present a sound and complete compositional semantics, structured around certain abstractions of proof nets, for proofsearch computation in a linear logicbased language. The model captures the interaction of agents in terms of the actions they engage into and of the dynamic creation of names. The model is adequate for reasoning about a notion of operational equivalence. We will also suggest how a partial order semantics can be derived from the present approach. 1
Proof of {Proof Net Semantics of Proof Search Computation Lu'is Caires and Lu'is Monteiro}
, 1997
"... A Proof of: We present a sound and complete compositional semantics for proofsearch computation in a linear logicbased language structured around certain abstractions of proof nets. The model captures the interaction of agents in terms of the actions they engage into and of the dynamic creation of ..."
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A Proof of: We present a sound and complete compositional semantics for proofsearch computation in a linear logicbased language structured around certain abstractions of proof nets. The model captures the interaction of agents in terms of the actions they engage into and of the dynamic creation of names. The model can also be shown adequate for reasoning about a notion of operational equivalence. We will also suggest how a partial order semantics can be derived from the present approach. 1
Labelled Deduction Labelled Deduction
"... In this paper, we propose new labelled proof systems to analyse the intuitionistic provability in classical and linear logics. An important point is to understand how search in a nonclassical logic can be viewed as a perturbation of search in classical logic. Therefore, suitable characterizations o ..."
Abstract
 Add to MetaCart
In this paper, we propose new labelled proof systems to analyse the intuitionistic provability in classical and linear logics. An important point is to understand how search in a nonclassical logic can be viewed as a perturbation of search in classical logic. Therefore, suitable characterizations of intuitionistic provability and related labelled sequent calculi are defined for linear logic. An alternative approach, based on the notion of proofnet and on the definition of suitable labelled classical proofnets, allows to directly study the intuitionistic provability by constructing intuitionistic proofnets for sequents of classical linear logic. Keywords: Proof theory, intuitionistic logic, linear logic, labelled sequent calculus, proofnets, automated deduction. 1. INTRODUCTION Many proofsearch methods (sequent calculus, tableaux, resolution, connections) have been naturally developed in classical logic (CL) with a view 1 2 LABELLED DEDUCTION to avoiding the possible redundanc...