Proof nets for multiplicative cyclic linear logic and Lambek calculus
نویسندگان
چکیده
منابع مشابه
Proof Nets for Multiplicative Cyclic Linear Logic and Lambek Calculus
This paper presents a simple and intuitive syntax for proof nets of the multiplicative cyclic fragment (McyLL) of linear logic (LL). The proposed correctness criterion for McyLL proof nets can be considered as the non-commutative counterpart of the famous Danos contraction criterion for proof nets of the pure multiplicative fragment (MLL) of LL. Unlike the most part of current syntaxes for non-...
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Grishin’s generalization of Lambek’s Syntactic Calculus combines a non-commutative multiplicative conjunction and its residuals (product, left and right division) with a dual family: multiplicative disjunction, right and left difference. Interaction between these two families takes the form of linear distributivity principles. We study proof nets for LG and the correspondence between these nets...
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We present a novel way of using proof nets for the multimodal Lambek calculus, which provides a general treatment of both the unary and binary connectives. We also introduce a correctness criterion which is valid for a large class of structural rules and prove basic soundness, completeness and cut elimination results. Finally, we will present a correctness criterion for the original Lambek calc...
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We provide an alternative proof of the sequentialisation theorem for proof nets of multiplicative linear logic. Namely, we show how a proof net can be transformed into a sequent calculus proof simply by properly adding to it some special edges, called sequential edges, which express the sequentiality constraints given by sequent calculus. © 2008 Elsevier B.V. All rights reserved.
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In this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting...
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ژورنال
عنوان ژورنال: Mathematical Structures in Computer Science
سال: 2019
ISSN: 0960-1295,1469-8072
DOI: 10.1017/s0960129518000300