Results 1 to 10 of about 160,476 (167)
On the Lambek Calculus with an Exchange Modality [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule.
Jiaming Jiang +2 more
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Relational Models for the Lambek Calculus with Intersection and Constants [PDF]
Logical Methods in Computer Science, 2023 We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant without constants and a restriction which disallows empty antecedents, Andreka and Mikulas (1994 ...
Stepan L. Kuznetsov
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Command injection attacks, continuations, and the Lambek calculus [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the Lambek calculus,
Hayo Thielecke
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Complexity of Nonassociative Lambek Calculus with Classical and Intuitionistic Logic
Bulletin of the Section of LogicThe Nonassociative Lambek Calculus (NL) represents a logic devoid of the structural rules of exchange, weakening, and contraction, and it does not presume the associativity of its connectives. Its finitary consequence relation is decidable in polynomial
Paweł Płaczek
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Normalization by Evaluation for the Lambek Calculus [PDF]
Non-Classical Logic. Theory and Applications, 2022 The syntactic calculus of Lambek is a deductive system for the multiplicative fragment of intuitionistic non-commutative linear logic. As a fine-grained calculus of resources, it has many applications, mostly in formal computational investigations of ...
Niccolò Veltri
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Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended Abstract) [PDF]
Electronic Proceedings in Theoretical Computer Science, 2021 We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality, which has a limited version of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with
Lachlan McPheat +3 more
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Multimodality in the Hypergraph Lambek Calculus [PDF]
AMSLO@ESSLLI, 2023 The multimodal Lambek calculus is an extension of the Lambek calculus that includes several product operations (some of them being commutative or/and associative), unary modalities, and corresponding residual implications.
Tikhon Pshenitsyn
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Axioms, 2023 Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a non-associative binary operator in RBL.
Zhe Lin, Minghui Ma
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COMPLEXITY OF THE INFINITARY LAMBEK CALCULUS WITH KLEENE STAR [PDF]
The Review of Symbolic Logic, 2020 We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega $ -rule, and prove that the derivability problem in this calculus is $\Pi _1^0$
S. Kuznetsov
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One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity
Bulletin of the Section of Logic, 2021 Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic.
Paweł Płaczek
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