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296,198
Subnets of Proofnets in MLL
, 1994
"... The paper studies the properties of the subnets of proofnets. Very simple proofs are obtained of known results on proofnets for MLL \Gamma , Multiplicative Linear Logic without propositional constants. Contents 1 Preface 1 2 Proof Nets for Propositional MLL \Gamma 3 2.1 Propositional Proof S ..."
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Cited by 2 (0 self)
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The paper studies the properties of the subnets of proofnets. Very simple proofs are obtained of known results on proofnets for MLL \Gamma , Multiplicative Linear Logic without propositional constants. Contents 1 Preface 1 2 Proof Nets for Propositional MLL \Gamma 3 2.1 Propositional Proof
Generation with Semantic Proof Nets
"... Categorial grammars and Lambek calculus found a nice embedding in Linear Logic, and a lot of work have presented proof nets uses for linguistic purposes, with a special look at proof nets for Lambek calculus. But they have mainly explored the syntactic capabilities of proof nets, describing parsing ..."
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Categorial grammars and Lambek calculus found a nice embedding in Linear Logic, and a lot of work have presented proof nets uses for linguistic purposes, with a special look at proof nets for Lambek calculus. But they have mainly explored the syntactic capabilities of proof nets, describing parsing
Coherence of ProofNet Categories
, 2005
"... The notion of proofnet category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A coh ..."
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The notion of proofnet category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A
Parsing mell proof nets
 In TLCA
, 1997
"... We propose a new formulation for full (weakening and constants included) multiplicative and exponential (MELL) proof nets, allowing a complete set of rewriting rules to parse them. The recognizing grammar de ned by such a rewriting system (con uent and strong normalizing on the new proof nets) gives ..."
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Cited by 8 (3 self)
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We propose a new formulation for full (weakening and constants included) multiplicative and exponential (MELL) proof nets, allowing a complete set of rewriting rules to parse them. The recognizing grammar de ned by such a rewriting system (con uent and strong normalizing on the new proof nets
Proof Nets and Explicit Substitutions
 Mathematical Structures in Computer Science
, 2000
"... We refine the simulation technique introduced in [10] to show strong normalization of calculi with explicit substitutions via termination of cut elimination in proof nets [12]. We first propose a notion of equivalence relation for proof nets that extends the one in [9], and we show that cut elimina ..."
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Cited by 11 (2 self)
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We refine the simulation technique introduced in [10] to show strong normalization of calculi with explicit substitutions via termination of cut elimination in proof nets [12]. We first propose a notion of equivalence relation for proof nets that extends the one in [9], and we show that cut
From ProofNets to Interaction Nets
 Advances in Linear Logic
, 1994
"... Introduction If we consider the interpretation of proofs as programs, say in intuitionistic logic, the question of equality between proofs becomes crucial: The syntax introduces meaningless distinctions whereas the (denotational) semantics makes excessive identifications. This question does not hav ..."
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Cited by 73 (1 self)
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not have a simple answer in general, but it leads to the notion of proofnet, which is one of the main novelties of linear logic. This has been already explained in [Gir87] and [GLT89]. The notion of interaction net introduced in [Laf90] comes from an attempt to implement the reduction of these proofnets
Concurrent Programming as Proof Net Construction
 Mathematical Structures in Computer Science
, 1997
"... this paper Concurrent Programming as Proof Net Construction 5 1.2. Process computations as proof nets ..."
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this paper Concurrent Programming as Proof Net Construction 5 1.2. Process computations as proof nets
Proof Nets for Intuitionistic Logic
 SAARBRÜCKEN, GERMANY
, 2006
"... Until the beginning of the 20th century, there was no way to reason formally about proofs. In particular, the question of proof equivalence had never been explored. When Hilbert asked in 1920 for an answer to this very question in his famous program, people started looking for proof formalizations.
..."
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proofs in intuitionistic and classical logic.
However, natural deduction only works well for intuitionistic logic. This is why Girard invented proof nets in 1986 as an analog to natural deduction for (the multiplicative fragment of) linear logic. Their universal structure made proof nets also interesting
Proof Nets and the λcalculus
 Linear Logic in Computer Science, 65–118
, 2004
"... In this survey we shall present the main results on proof nets for the Multiplicative and Exponential fragment of Linear Logic (MELL) and discuss their connections with λcalculus. The survey ends with a short introduction to sharing reduction. The part on proof nets and on the encoding of λterms ..."
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In this survey we shall present the main results on proof nets for the Multiplicative and Exponential fragment of Linear Logic (MELL) and discuss their connections with λcalculus. The survey ends with a short introduction to sharing reduction. The part on proof nets and on the encoding of λ
Lexicalized ProofNets and TAGs
 Logical Aspects of Computational Linguistics, LACL‘98, selected papers’, number 2014 in ‘LNCS/LNAI
, 1998
"... Introduction First introduced by [Ret93], pomset linear logic can deal with linguistic aspects by inducing a partial order on words. [LR95] uses this property: it defines modules (or partial proofnets) which consist in entries for words, describing both the category of the word and its behavior wh ..."
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Introduction First introduced by [Ret93], pomset linear logic can deal with linguistic aspects by inducing a partial order on words. [LR95] uses this property: it defines modules (or partial proofnets) which consist in entries for words, describing both the category of the word and its behavior
Results 1  10
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296,198