Academic literature on the topic 'Multiplicative-additive linear logic'
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Journal articles on the topic "Multiplicative-additive linear logic"
MAZZA, DAMIANO. "Infinitary affine proofs." Mathematical Structures in Computer Science 27, no. 5 (July 7, 2015): 581–602. http://dx.doi.org/10.1017/s0960129515000298.
Full textLafont, Yves. "The undecidability of second order linear logic without exponentials." Journal of Symbolic Logic 61, no. 2 (June 1996): 541–48. http://dx.doi.org/10.2307/2275674.
Full textCockett, J. R. B., and C. A. Pastro. "A Language For Multiplicative-additive Linear Logic." Electronic Notes in Theoretical Computer Science 122 (March 2005): 23–65. http://dx.doi.org/10.1016/j.entcs.2004.06.049.
Full textO'Hearn, Peter W., and David J. Pym. "The Logic of Bunched Implications." Bulletin of Symbolic Logic 5, no. 2 (June 1999): 215–44. http://dx.doi.org/10.2307/421090.
Full textCHAUDHURI, KAUSTUV. "Expressing additives using multiplicatives and subexponentials." Mathematical Structures in Computer Science 28, no. 5 (November 21, 2016): 651–66. http://dx.doi.org/10.1017/s0960129516000293.
Full textHughes, Dominic J. D., and Rob J. Van Glabbeek. "Proof nets for unit-free multiplicative-additive linear logic." ACM Transactions on Computational Logic 6, no. 4 (October 2005): 784–842. http://dx.doi.org/10.1145/1094622.1094629.
Full textCHAUDHURI, KAUSTUV, JOËLLE DESPEYROUX, CARLOS OLARTE, and ELAINE PIMENTEL. "Hybrid linear logic, revisited." Mathematical Structures in Computer Science 29, no. 8 (April 22, 2019): 1151–76. http://dx.doi.org/10.1017/s0960129518000439.
Full textOkada, Mitsuhiro, and Kazushige Terui. "The finite model property for various fragments of intuitionistic linear logic." Journal of Symbolic Logic 64, no. 2 (June 1999): 790–802. http://dx.doi.org/10.2307/2586501.
Full textHamano, Masahiro. "A MALL geometry of interaction based on indexed linear logic." Mathematical Structures in Computer Science 30, no. 10 (November 2020): 1025–53. http://dx.doi.org/10.1017/s0960129521000062.
Full textBucciarelli, Antonio, and Thomas Ehrhard. "On phase semantics and denotational semantics in multiplicative–additive linear logic." Annals of Pure and Applied Logic 102, no. 3 (April 2000): 247–82. http://dx.doi.org/10.1016/s0168-0072(99)00040-8.
Full textDissertations / Theses on the topic "Multiplicative-additive linear logic"
Di, Guardia Rémi. "Identity of Proofs and Formulas using Proof-Nets in Multiplicative-Additive Linear Logic." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0050.
Full textThis study is concerned with the equality of proofs and formulas in linear logic, with in particular contributions for the multiplicative-additive fragment of this logic. In linear logic, and as in many other logics (such as intuitionistic logic), there are two transformations on proofs: cut-elimination and axiom-expansion. One often wishes to identify two proofs related by these transformations, as it is the case semantically (in a categorical model for instance). This situation is similar to the one in the λ-calculus where terms are identified up to β-reduction and η-expansion, operations that, through the prism of the Curry-Howard correspondence, are related respectively to cut-elimination and axiom-expansion. We show here that this identification corresponds exactly to identifying proofs up to rule commutation, a third well-known operation on proofs which is easier to manipulate. We prove so only in multiplicative-additive linear logic, even if we conjecture such a result holds in full linear logic.Not only proofs but also formulas can be identified up to cut-elimination and axiom-expansion. Two formulas are isomorphic if there are proofs between them whose compositions yield identities, still up to cut-elimination and axiom-expansion. These formulas are then really considered to be the same, and every use of one can be replaced with one use of the other. We give an equational theory characterizing exactly isomorphic formulas in multiplicative-additive linear logic. A generalization of an isomorphism is a retraction, which intuitively corresponds to a couple of formulas where the first can be replaced by the second -- but not necessarily the other way around, contrary to an isomorphism. Studying retractions is more complicated, and we characterize retractions to an atom in the multiplicative fragment of linear logic.When studying the two previous problems, the usual syntax of proofs from sequent calculus seems ill-suited because we consider proofs up to rule commutation. Part of linear logic can be expressed in a better adapted syntax in this case: proof-nets, which are graphs representing proofs quotiented by rule commutation. This syntax was an instrumental tool for the characterization of isomorphisms and retractions. Unfortunately, proof-nets are not (or badly) defined with units. Concerning our issues, this restriction leads to a study of the unit-free case by means of proof-nets with the crux of the demonstration, preceded by a work in sequent calculus to handle the units. Besides, this thesis also develops part of the theory of proof-nets by providing a simple proof of the sequentialization theorem, which relates the two syntaxes of proof-net and sequent calculus, substantiating that they describe the same underlying objects. This new demonstration is obtained as a corollary of a generalization of Yeo's theorem. This last result is fully expressed in the theory of edge-colored graphs, and allows to recover proofs of sequentialization for various definitions of proof-nets. Finally, we also formalized proof-nets for the multiplicative fragment of linear logic in the proof assistant Coq, with notably an implementation of our new sequentialization proof
Book chapters on the topic "Multiplicative-additive linear logic"
Maieli, Roberto. "Retractile Proof Nets of the Purely Multiplicative and Additive Fragment of Linear Logic." In Logic for Programming, Artificial Intelligence, and Reasoning, 363–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75560-9_27.
Full textWood, James, and Robert Atkey. "A Framework for Substructural Type Systems." In Programming Languages and Systems, 376–402. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99336-8_14.
Full textAbrusci, Vito Michele, and Roberto Maieli. "Cyclic Multiplicative-Additive Proof Nets of Linear Logic with an Application to Language Parsing." In Formal Grammar, 43–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-53042-9_3.
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