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Syntactic concept lattice models for infinitary action logic
P. 93–107.
Keywords: concept latticesLambek calculusисчисление Ламбекаформальные понятиялогика действийInfinitary Action Logic
Publication based on the results of:
In book
Vol. 14672: Lecture Notes in Computer Science. , Cham: Springer, 2024.
Ignatov D. I., , in: 11th International Conference, AIST 2023, Yerevan, Armenia, September 28–30, 2023, Revised Selected Papers. Analysis of Images, Social Networks and Texts. Lecture Notes in Computer Science (LNCS, volume 14486).: Cham: Springer, 2024. P. 349 – 361.
This paper dates back to the asymptotic solutions of Rota’s problem on the size of maximum antichain in the set partition lattice by Canfield and Harper and others. The knowledge of asymptotic coefficients could pave the way to the asymptotic solutions of such problems as (maximal) antichain counting in partition lattices. In addition to our ...
Added: January 23, 2026
Ignatov D. I., , in: FCA4AI 2024: The 12th International Workshop "What can FCA do for Artificial Intelligence?", October 19 2024, Santiago de Compostela, SpainVol. 3911.: CEUR Workshop Proceedings, 2024. P. 27–38.
The paper formulates Zarankiewicz problem in terms of formal contexts as follows: What is z(m, n; s, t), the
largest size of the incidence relation of a formal context with m objects and n attributes, for which there is no a
formal concept with the given extent s and t intent sizes and larger? Exact formulas for ...
Added: January 23, 2026
Kemgne M. W., Njionou B. B., Ignatov D. I. et al., International Journal of Approximate Reasoning 2025 Vol. 186 Article 109527
This paper introduces cooperative games with transferable utilities and fuzzy characteristic functions on concept lattices. While previous works have independently addressed games with fuzzy payoffs and games restricted to structured coalition systems such as lattices, our approach combines both perspectives. We consider cooperative settings where coalition formation is constrained by a concept lattice structure, and ...
Added: January 23, 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
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
Ignatov D. I., , in: LNAI 14133: 28th International Conference on Conceptual Structures, ICCS 2023, Berlin, Germany, September 11–13, 2023, Proceedings. Graph-Based Representation and Reasoning.: Berlin: Springer, 2023. P. 56–69.
Set partitions and partition lattices are well-known objects in combinatorics and play an important role as a search space in many applied problems including ensemble clustering. Searching for antichains in such lattices is similar to that of in Boolean lattices. Counting the number of antichains in Boolean lattices is known as the Dedekind problem. In ...
Added: November 23, 2023
S. M. Dudakov, Karlov B. N., S. L. Kuznetsov et al., Algebra and Logic 2021 Vol. 60 No. 5 P. 308–326
The Lambek calculus with the unit can be defined as the atomic theory (algebraic logic) of the class of residuated monoids. This calculus, being a theory of a broader class of algebras than Heyting ones, is weaker than intuitionistic logic. Namely, it lacks structural rules: permutation, contraction, and weakening. We consider two extensions of the ...
Added: November 12, 2023
Ignatov D. I., Kwuida L., Annals of Mathematics and Artificial Intelligence 2022 Vol. 90 No. 11 P. 1197–1222
We propose the usage of two power indices from cooperative game theory and public choice theory for ranking attributes of closed sets, namely intents of formal concepts (or closed itemsets). The introduced indices are related to extensional concept stability and are also based on counting of generators, especially of those that contain a selected attribute. ...
Added: January 31, 2023
Kanovich M., Kuznetsov Stepan G., Kuznetsov S. et al., Studies in Computational Intelligence 2021 Vol. 999 P. 1–24
CatLog is a categorial grammar parser/theorem-prover
developed by Glyn Morrill and his co-authors. CatLog is based on an
extension of Lambek calculus. A distinctive feature of this extension is
the usage of brackets for controlled non-associativity and a subexponential
modality whose contraction rule interacts with bracketing in a
sophisticated way. We consider two variants of the calculus, appearing in
different versions ...
Added: December 14, 2021
Kanovich M., Kuznetsov S., Scedrov A., 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 ...
Added: December 4, 2021
Slavnov S. A., Journal of Logic and Computation 2022 Vol. 32 No. 3 P. 479–517
We consider tensor grammars, which are an example of ‘commutative’ grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface representation of abstract categorial grammars (ACG) in the sense that derivations of ACG translate to derivations of tensor grammars and this translation is isomorphic on the level of string ...
Added: October 21, 2021
Dudyrev E., Kuznetsov S., , in: Formal Concept Analysis: 16th International Conference, ICFCA 2021, Strasbourg, France, June 29 – July 2, 2021, Proceedings.: Springer, 2021. Ch. 16 P. 252–260.
Added: September 28, 2021
Springer, 2021.
This book constitutes the proceedings of the 16th International Conference on Formal Concept Analysis, ICFCA 2021, held in Strasbourg, France, in June/July 2021.
The 14 full papers and 5 short papers presented in this volume were carefully reviewed and selected from 32 submissions. The book also contains four invited contributions in full paper length.
The research part ...
Added: July 10, 2021
Kanovich M., Kuznetsov S., Scedrov A., Journal of Logic, Language and Information 2021 Vol. 30 No. 1 P. 31–88
We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill’s calculi, and focus on their fragments including multiplicative (Lambek) connectives, additive conjunction and disjunction, brackets and bracket modalities, and the ! subexponential modality. For ...
Added: November 25, 2020
Kuznetsov S., , in: Logic, Language, and Security. Essays Dedicated to Andre Scedrov on the Occasion of His 65th BirthdayIssue 12300.: Cham: Springer, 2020. P. 3–16.
Infinitary action logic is an extension of the multiplicative-additive Lambek calculus with Kleene iteration, axiomatized by an 𝜔-rule. Buszkowski and Palka (2007) show that this logic is \(\Pi^0_1\)-complete. As shown recently by Kuznetsov and Speranski, the extension of infinitary action logic with the exponential modality is much harder: \(\Pi^1_1\)-complete. The raise of complexity is of ...
Added: November 25, 2020
Ignatov D. I., Kwuida L., , in: Ontologies and Concepts in Mind and Machine. 25th International Conference on Conceptual Structures, ICCS 2020.: Springer, 2020. P. 90–102.
Among the family of rule-based classification models, there are classifiers based on conjunctions of binary attributes. For example, the JSM-method of automatic reasoning (named after John Stuart Mill) was formulated as a classification technique in terms of intents of formal concepts as classification hypotheses. These JSM-hypotheses already represent an interpretable model since the respective conjunctions ...
Added: October 30, 2020