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Proof nets for the Lambekcalculus — an overview
 Proceedings of the Third Roma Workshop ”Proofs and Linguistic Categories
, 1996
"... 1 Introduction: the interest of proof nets for categorial grammar There are both linguistic and mathematical reasons for studying proof nets the perspective of categorial grammar. It is now well known that the Lambek calculus corresponds to intuitionnistic noncommutative multiplicative linear logic ..."
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Cited by 14 (2 self)
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1 Introduction: the interest of proof nets for categorial grammar There are both linguistic and mathematical reasons for studying proof nets the perspective of categorial grammar. It is now well known that the Lambek calculus corresponds to intuitionnistic noncommutative multiplicative linear logic — with no empty antecedent, to be absolutely precise. As natural deduction underlines the constructive contents of intuitionistic
CLASSICAL NONASSOCIATIVE LAMBEK CALCULUS
"... We introduce nonassociative linear logic, which may be seen as the classical version of the nonassociative Lambek calculus. We define its sequent calculus, its theory of proof nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polyno ..."
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Cited by 9 (1 self)
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We introduce nonassociative linear logic, which may be seen as the classical version of the nonassociative Lambek calculus. We define its sequent calculus, its theory of proof nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial.
The Shuffle Hopf Algebra and Noncommutative Full Completeness
, 1999
"... We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformati ..."
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Cited by 8 (3 self)
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We present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffle algebra. Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cutfree proofs in CyLL+MIX. This can be viewed as a fully faithful representation of a free *autonomous category, canonically enriched over vector spaces. This paper