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Some new results in monadic second-order arithmetic
Computability. 2015. Vol. 4. No. 2. P. 159–174.
Knyazeva H., МЕТОД: Московский ежегодник трудов из обществоведческих дисциплин 2025 Т. 5 № 4 С. 176–182
This article analyzes the creative personality and thinking style of Vladimir Ivanovich Arshinov, as well as his distinctive contribution to the philosophy of science – the concept of complexity as an observer embedded in the complexity of the world. Arshinov conceptualized complexity as a key characteristic of self-organizing systems within the context of post-non-classical science ...
Added: October 1, 2026
Kuznetsov S., Pshenitsyn T., Speranski S. O., Journal of Symbolic Logic 2025 Article jsl.2025.16
The class of all ∗-continuous Kleene algebras, whose description includes an infinitary condition on the iteration operator, plays an important role in computer science. The complexity of reasoning in such algebras — ranging from the equational theory to the Horn one, with restricted fragments of the latter in between — was analyzed by Kozen (2002). This ...
Added: August 12, 2026
Speranski S. O., Математические заметки 2026 Т. 120 № 3 С. 470–483
We show that, in terms of closure ordinals, many infinitary calculi for ‘first-order’ logics of probability (i.e., for languages similar to those in [Abadi & Halpern 1994]) are as hard as possible: the corresponding closure ordinals coincide with the least non-constructive ordinal, denoted by $\omega_1^{\mathrm{CK}}$. ...
Added: August 12, 2026
Speranski S. O., Grefenshtein A., Izvestiya. Mathematics 2026 Vol. 90 No. 4 P. 754–775
The article is concerned with Halpern's first-order logics of probability, which we denote by L_1 and L_2 – the first of these deals with probability distributions on the domain, while the second employs distributions on external sets of possible worlds. The proofs of [Abadi & Halpern 1994] of the complexity lower bound results for L_1 and L_2 ...
Added: August 12, 2026
David J. L., Leonid Grinin, Korotayev A., , in: Complexity in Universal Evolution. A Big History Perspective.: Springer, 2026. Ch. 22 P. 585–608.
This collective monograph explores focus on complexity aspects in Big History against the background of complexity growth in the Universe, on our planet, and in biological, social, and cultural systems. Complexity growth is regarded as the connecting thread of evolutionary development and as a leading trend of Big History. The cosmic development chapters examine symmetries ...
Added: August 10, 2026
Korotayev A., , in: Complexity in Universal Evolution. A Big History Perspective.: Springer, 2026. Ch. 13 P. 359–409.
We have undertaken an attempt to propose a periodization of the Big History Biosocial (Anthropogenesis) Era on the basis of the most recent scientific data. This periodization is complexity-based, that is, the boundaries of the identified epochs are marked with complexity jumps, that is, in our case, such phase transitions that result in significant increases ...
Added: August 10, 2026
Leonid Grinin, Alexander M., Korotayev A., , in: Complexity in Universal Evolution. A Big History Perspective.: Springer, 2026. Ch. 12 P. 283–355.
In the first half of this chapter, Grinin et al. survey general similarities and differences between biological and social macroevolution. They undertake a systematic comparison between biological and social evolution at different levels of analysis and in various aspects, formulating a considerable number of general principles and rules of evolution, and working to develop a ...
Added: August 10, 2026
David J. L., Leonid Grinin, Korotayev A., , in: Complexity in Universal Evolution. A Big History Perspective.: Springer, 2026. Ch. 1 P. 1–25.
Complexity is widely acknowledged as a foundational and pivotal concept in Big History, offering a unifying lens through which to examine the emergence and development of systems—from particles and galaxies to life, civilizations, and beyond. Yet, despite its centrality, major gaps remain in how we define, measure, and interpret complexity across different phases and scales. ...
Added: August 10, 2026
Pahomov F., Zapryagaev A., Logic Journal of the IGPL 2026 Vol. 34 No. 4 Article jzag045
We prove the linear orders first-order definable in the standard model (Z;<,+) of Presburger arithmetic are exactly those that are (Z;<,+)-definably embeddable into the lexicographic ordering on Z^n for some n. ...
Added: July 16, 2026
Yerbolova A. S., Tomashchuk K., Kogan A. et al., Complexity 2026 Vol. 2026 No. 1 Article 5519690
Tis paper presents a novel approach to analyzing and grouping natural languages based on the degree of their chaoticity. It clusters 52 languages from 18 language families, according to the value of the entropy–complexity pair, to reveal the chaotic properties of semantic trajectories. Te obtained clusters appear to be closely correlated with the family of ...
Added: February 16, 2026
Speranski S. O., Journal of Logic and Computation 2013 Vol. 23 No. 5 P. 1035–1055
In the present article, the quantifiers over propositions are first introduced into the language for reasoning about probability, then the complexity issues for validity problems dealing with the corresponding hierarchy of probabilistic sentences are investigated. We prove, among other things, the $\Pi^1_1$-completeness for the general validity and also indicate the least level in the hierarchy ...
Added: December 27, 2025
Speranski S. O., Archive for Mathematical Logic 2013 Vol. 52 No. 5–6 P. 507–516
We carry out a study of definability issues in the standard models of Presburger and Skolem arithmetics (henceforth referred to simply as Presburger and Skolem arithmetics, for short, because we only deal with these models, not the theories, thus there is no risk of confusion) supplied with free unary predicates — which are strongly related to definability in ...
Added: December 27, 2025
Speranski S. O., Studia Logica 2017 Vol. 105 No. 2 P. 407–429
The paper contains a survey on the complexity of various truth hierarchies arising in Kripke’s theory. I present some new arguments, and use them to obtain a number of interesting generalisations of known results. These arguments are both relatively simple, involving only the basic machinery of constructive ordinals, and very general. ...
Added: December 26, 2025
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
Speranski S. O., Logic Journal of the IGPL 2025 Vol. 33 No. 2 Article jzae042
This paper is concerned with a two-sorted probabilistic language, denoted by QPL, which contains quantifiers over events and over reals, and can be viewed as an elementary language for reasoning about probability spaces. The fragment of QPL containing only quantifiers over reals is a variant of the well-known ‘polynomial’ language from [Fagin et al. 1990, Section 6]. ...
Added: December 26, 2025
Speranski S. O., Logic Journal of the IGPL 2025 Vol. 33 No. 3 Article jzae114
We shall be concerned with two natural expansions of the quantifier-free ‘polynomial’ probability logic of [Fagin et al. 1990]. One of these, denoted by QPL-e, is obtained by adding quantifiers over arbitrary events, and the other, denoted by p-QPL-e, uses quantifiers over propositional formulas — or equivalently, over events expressible by such formulas. The earlier proofs ...
Added: December 26, 2025
LePoire D., Grinin L. E., Korotayev A., Journal of Big History 2025 Vol. 8 No. 3 P. 98–139
Building on foundational work in systems theory, thermodynamics, and evolutionary theory, this paper argues that complexity can serve as a conceptual bridge across disciplines. It explores the role of complexity dynamics in Big History through an integrative theoretical framework that spans physical, chemical, geological, biological, social, cognitive, and civilizational domains. By examining how complexity emerges, ...
Added: November 1, 2025
Yury Semenov, Oleg Sukhoroslov, , in: Mathematical Optimization Theory and Operations Research 24th International Conference, MOTOR 2025, Novosibirsk, Russia, July 7–11, 2025, ProceedingsVol. 15681.: Switzerland: Springer, 2025. P. 317–331.
Added: September 17, 2025
Arzhantsev I., Functional Analysis and Its Applications 1997 Vol. 31 No. 4 P. 278–280
Let a connected reductive group G act on a normal affine variety X with the generic stabilizer H, let the complexity of this action be one, and let the categorial quotient X//G be one-dimensional. Then the closure of any G-orbit in X is normal. ...
Added: June 13, 2025
Cham: Springer, 2020.
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the Eighth International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2019), which took place in Lisbon, ...
Added: February 27, 2024
Marina Boykova, Knyazeva H., Salazkin M., Foresight and STI Governance 2023 Vol. 17 No. 4 P. 80–91
The challenges the futures studies face are particularly complex, interconnected, and contradictory, and cannot be resolved using linear approaches. Prognostic science needs tools matching the new contextual complexity, which would allow to capture a much wider range of driving forces, and their potential effects, in a non-linear perspective, to improve the accuracy of forecasts and ...
Added: January 25, 2024