On Lambek’s Restriction in the Presence of Exponential Modalities

We introduce infinitary action logic with exponentiation — that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allow some of the structural rules (contraction, weakening, permutation). The logic is presented in the form of an infinitary sequent calculus. We prove cut elimination and, in the case ...

Добавлено: 26 декабря 2025 г.

Infinitary action logic with multiplexing

Кузнецов С. Л., Сперанский С. О., Studia Logica 2023 Vol. 111 No. 2 P. 251–280

Infinitary action logic can be naturally expanded by adding exponential and subexponential modalities from linear logic. In this article we shall develop infinitary action logic with a subexponential that allows multiplexing (instead of contraction). Both non-commutative and commutative versions of this logic will be considered, presented as infinitary sequent calculi. We shall prove cut admissibility ...

Добавлено: 26 декабря 2025 г.

Craig's trick and a non-sequential system for the Lambek calculus and its fragments

Кузнецов С. Л., Lugovaya V., Рыжова А. А., Logic Journal of the IGPL 2019 Vol. 27 No. 3 P. 252–266

Добавлено: 1 мая 2025 г.

Syntactic concept lattice models for infinitary action logic

Stepan L. Kuznetsov, , in: Logic, Language, Information, and Computation: 30th International Workshop, WoLLIC 2024, Bern, Switzerland, June 10–13, 2024, ProceedingsVol. 14672: Lecture Notes in Computer Science.: Cham: Springer, 2024. P. 93–107.

Добавлено: 12 июня 2024 г.

Making first order linear logic a generating grammar

Sergey Slavnov, Logical Methods in Computer Science 2023 Vol. 19 No. 4

Добавлено: 20 декабря 2023 г.

COMPLEXITY OF LAMBEK CALCULI WITH MODALITIES AND OF TOTAL DERIVABILITY IN GRAMMARS

S. M. Dudakov, Karlov B. N., S. L. Kuznetsov и др., Algebra and Logic 2021 Vol. 60 No. 5 P. 308–326

Добавлено: 12 ноября 2023 г.

Non-associative, non-commutative multi-modal linear logic

Blaisdell E., Канович М. И., Stepan L. Kuznetsov и др., , in: Automated Reasoning: 11th International Joint Conference, IJCAR 2022, Haifa, Israel, August 8–10, 2022, ProceedingsVol. 13385.: Cham: Springer, 2022. P. 449–467.

Добавлено: 7 августа 2022 г.

Decidable Fragments of Calculi Used in CatLog

Канович М. И., Kuznetsov Stepan G., Кузнецов С. Л. и др., Studies in Computational Intelligence 2021 Vol. 999 P. 1–24

Добавлено: 14 декабря 2021 г.

Language models for some extensions of the Lambek calculus

Канович М. И., Кузнецов С. Л., Щедров А., Information and Computation 2022 Vol. 287 Article 104760

Добавлено: 4 декабря 2021 г.

Linear logic in normed cones: probabilistic coherence spaces and beyond

Sergey Slavnov, Mathematical Structures in Computer Science 2021 Vol. 31 No. 5 P. 495–534

Добавлено: 16 ноября 2021 г.

On embedding Lambek calculus into commutative categorial grammars

Славнов С. А., Journal of Logic and Computation 2022 Vol. 32 No. 3 P. 479–517

Добавлено: 21 октября 2021 г.

Cobordisms and Commutative Categorial Grammars

Sergey Slavnov, Journal of Cognitive Science 2021 Vol. 22 No. 2 P. 68–91

Добавлено: 2 октября 2021 г.

Undecidability of the logic of partial quasiary predicates

Рыбаков М. Н., Shkatov D., Logic Journal of the IGPL 2022 Vol. 30 No. 3 P. 519–533

Добавлено: 29 мая 2021 г.

The multiplicative-additive Lambek calculus with subexponential and bracket modalities

Канович М. И., Кузнецов С. Л., Щедров А., Journal of Logic, Language and Information 2021 Vol. 30 No. 1 P. 31–88

Добавлено: 25 ноября 2020 г.

A \(\Pi^0_1\)-bounded fragment of infinitary action logic with exponential

Кузнецов С. Л., , in: Logic, Language, and Security. Essays Dedicated to Andre Scedrov on the Occasion of His 65th BirthdayIssue 12300.: Cham: Springer, 2020. P. 3–16.

Добавлено: 25 ноября 2020 г.

Algorithmic properties of first-order modal logics of the natural number line in restricted languages

Рыбаков М. Н., Shkatov D., , in: Advances in Modal LogicVol. 13.: College Publications, 2020. P. 523–539.

Добавлено: 27 августа 2020 г.

Algorithmic properties of first-order modal logics of finite Kripke frames in restricted languages

Рыбаков М. Н., Shkatov D., Journal of Logic and Computation 2020 Vol. 30 No. 7 P. 1305–1329

Добавлено: 27 августа 2020 г.

Soft subexponentials and multiplexing

Канович М. И., Кузнецов С. Л., Nigam V. и др., , in: Automated Reasoning, 10th International Joint Conference, IJCAR 2020, Part IVol. 12166.: Cham: Springer, 2020. P. 500–517.

Добавлено: 1 июля 2020 г.

Reconciling Lambek's restriction, cut-elimination, and substitution in the presence of exponential modalities

Канович М. И., Кузнецов С. Л., Щедров А., Journal of Logic and Computation 2020 Vol. 30 No. 1 P. 239–256

Добавлено: 1 июля 2020 г.