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Language models for some extensions of the Lambek calculus
Information and Computation. 2022. Vol. 287. Article 104760.
We investigate language interpretations of two extensions of the Lambek calculus: with additive conjunction and disjunction and with additive conjunction and the unit constant. For extensions with additive connectives, we show that conjunction and disjunction behave differently. Adding both of them leads to incompleteness due to the distributivity law. We show that with conjunction only no issues with distributivity arise. In contrast, there exists a corollary of the distributivity law in the language with disjunction only which is not derivable in the non-distributive system. Moreover, this difference keeps valid for systems with permutation and/or weakening structural rules, that is, intuitionistic linear and affine logics and affine multiplicative-additive Lambek calculus. For the extension of the Lambek calculus with the unit constant, we present a calculus which reflects natural algebraic properties of the empty word. We do not claim completeness for this calculus, but we prove undecidability for the whole range of systems extending this minimal calculus and sound w.r.t. language models. As a corollary, we show that in the language with the unit there exists a sequent that is true if all variables are interpreted by regular language, but not true in language models in general.
Publication based on the results of:
Chepovskiy A., Мастерская Печати Идей, 2026.
The textbook presents methods and algoгithms for automatic analysis
of соrроrа of texts in natural languages. It is intended fоr sfudenБ of
methods of processing texts in паtчrаl languages and creating training
arays of texts.
Fоr students, graduate students and researchers studying methods
of computational linguistics and word processing. ...
Added: August 1, 2026
Radomskii A., Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Уилкокс П., Romanov A., М.: ДМК Пресс, 2025.
Книга, которую вы держите в руках, продолжает серию «Книжная полка истового
инженера», которая издается при поддержке компании YADRO.
Данная книга представляет собой учебник по теоретическим основам продвинутой
функциональной верификации и содержит лучшие практики, используемые в настоящее
время. В ней подробно описана унифицированная методология верификации
(UVM) и раскрыты такие темы, как функциональный виртуальный прототип, функциональное
покрытие, утверждения, формальная верификация, тестбенчи, косимуляция,
эмуляция, аппаратное ...
Added: July 30, 2026
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234
Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing
interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications.
Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and
reason about. Here we build analytical representation for such ...
Added: July 28, 2026
Думкин Н. А., Alexandrov D., Прозорский М. А., Труды Института системного программирования РАН 2026 Т. 38 № 1 С. 255–274
A theoretically sound approach to adaptive client-side video fragment restoration is proposed using
machine learning and scene analysis methods. The method includes a formal problem statement, a finite-state
machine model for decision making, a restoration cost function, and a new stage in video preparation: scene
dynamics assessment followed by recording a feature in an HLS playlist. This feature ...
Added: July 27, 2026
Menovshchikov A., Ukhlov A., Rendiconti del Circolo Matematico di Palermo 2026 Vol. 75 Article 91
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These embeddings give the solvability of the Neumann spectral problem in this setting and provide estimates for the corresponding weighted Neumann eigenvalues. ...
Added: July 27, 2026
Menovshchikov A., Journal of Mathematical Sciences 2026 Vol. 298 P. 608–618
We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains. ...
Added: July 27, 2026
Cham: Springer, 2026.
This open access set, LNAI 16688-16689, constitutes the proceedings of the 13th International Joint Conference, IJCAR 2026, held in Lisbon, Portugal, during July 26–29, 2026.
The 41 full research papers and 8 short papers included in these two volumes were carefully reviewed and selected from 112 submissions. The papers cover the following topical sections:
Part I: Theorem ...
Added: July 26, 2026
Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026 Vol. 14 P. 2169–3536
This work presents a hierarchy of strictly local fault-tolerant routing algorithms for 3D mesh networks-on-chip, culminating in an algorithm that combines a live-neighbor selection rule with a bounded single-hop rollback mechanism. The proposed algorithms operate exclusively on immediate neighbor information, maintain O(1) per hop complexity, and require no global topology knowledge, additional virtual channels, or ...
Added: July 23, 2026
Pislyakov V., Вестник Томского государственного университета. Филология 2026 № 101 С. 175–192
This article examines the use of proverbs in academic texts—specifically, articles published in Russian research journals. For the experiment, ten proverbs were selected as the intersection of two fundamentally different paremiological surveys aimed at compiling lists of popular or common Russian proverbs. One of these surveys was conducted by the classic of paremiology, G.L. Permyakov, ...
Added: July 22, 2026
Association for Computing Machinery (ACM), 2026.
Wominjeka, and welcome to the 49th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR 2026), held in Melbourne | Naarm, Australia, from 20–24 July 2026. SIGIR 2026 takes place on the unceded lands of the Woi Wurrung and Boon Wurrung language groups of the eastern Kulin nation, and we pay our ...
Added: July 22, 2026
Korogod D., Shapeev A., Ivan S. Novikov, Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 2 Article 024104
We present two models with explicit long-range electrostatics in the form of Coulomb interactions. Both models include point charges depending on their local atomic environments, and the second model also conserves a total charge of an atomic system. We combine the proposed long-range models with the local moment tensor potential (MTP) and demonstrate that they ...
Added: July 22, 2026
Sozykin K., Rybin N., Chertkov A. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 113 No. 22 Article 224111
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through tensor train (TT) decomposition. Our ...
Added: July 22, 2026
Singapore: Springer, 2024.
Included in the following conference series:
INdAM: INdAM Meeting: Kolmogorov Operators and their Applications Workshop
Conference proceedings info: INdAM 2022
Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields.
This volume collects a selection of the talks given at the Cortona meeting by ...
Added: July 17, 2026
Stepan L. Kuznetsov, Journal of Logic and Computation 2026 Vol. 36 No. 1 Article exaf078
The linguistic applications of the Lambek calculus suggest its semantics over algebras of formal languages. A straightforward approach to construct such semantics indeed yields a brilliant completeness theorem (Pentus 1995, Ann. Pure Appl. Logic, 75, 179–213). However, extending the calculus with extra operations ruins completeness. In order to mitigate this issue, Wurm (2017, J. Logic Lang. Inf., ...
Added: January 14, 2026
Kuznetsov S., Speranski S. O., Annals of Pure and Applied Logic 2022 Vol. 173 No. 2 Article 103057
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 ...
Added: December 26, 2025
Kuznetsov S., Speranski S. O., 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 ...
Added: December 26, 2025
Kuznetsov S., Lugovaya V., Ryzhova A., Logic Journal of the IGPL 2019 Vol. 27 No. 3 P. 252–266
Added: May 1, 2025
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.
Added: June 12, 2024
Sergey Slavnov, Logical Methods in Computer Science 2023 Vol. 19 No. 4
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type calculus (ETTC). ETTC is a calculus of specific typed terms, which represent tuples of strings, more precisely bipartite graphs ...
Added: December 20, 2023