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An ‘elementary’ perspective on reasoning about probability spaces
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]. We shall prove that the QPL-theory of the Lebesgue measure on [0, 1] is decidable, and moreover, all atomless spaces have the same QPL-theory. Also we shall introduce the notion of elementary invariant for QPL, and use it to translate the semantics for QPL into the setting of elementary analysis. This will allow us to obtain further decidability results as well as to provide exact complexity upper bounds for a range of interesting undecidable theories.
Добавлено: 16 февраля 2026 г.
Сперанский С. О., 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 ...
Добавлено: 27 декабря 2025 г.
Сперанский С. О., 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 ...
Добавлено: 27 декабря 2025 г.
Сперанский С. О., 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. ...
Добавлено: 26 декабря 2025 г.
Сперанский С. О., Mathematical Structures in Computer Science 2017 Vol. 27 No. 8 P. 1581–1600
In this article we describe a bunch of probability logics with quantifiers over events, and develop primary techniques for proving computational complexity results (in terms of m-degrees) about these logics, mainly over discrete probability spaces. Also the article contains a comparison with some other probability logics and a discussion of interesting analogies with research in the metamathematics ...
Добавлено: 26 декабря 2025 г.
Кузнецов С. Л., Сперанский С. О., 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 ...
Добавлено: 26 декабря 2025 г.
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.
Сперанский С. О., Izvestiya. Mathematics 2025 Vol. 89 No. 3 P. 193–211
Let QPL-e expand the quantifier-free ‘polynomial’ probability logic of [Fagin et al. 1990] by adding quantifiers over arbitrary events; it can be viewed as a one-sorted elementary language for reasoning about probability spaces. We prove that the $\Sigma_2$-fragment of the QPL-e-theory of finite spaces is hereditarily undecidable. By earlier observations, this implies that $\Pi_2$ is the ...
Добавлено: 26 декабря 2025 г.
Сперанский С. О., 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 ...
Добавлено: 26 декабря 2025 г.
Добавлено: 1 ноября 2025 г.
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.
Добавлено: 17 сентября 2025 г.
Аржанцев И. В., Functional Analysis and Its Applications 1997 Vol. 31 No. 4 P. 278–280
Добавлено: 13 июня 2025 г.
Cham: Springer, 2020.
Добавлено: 27 февраля 2024 г.
Marina Boykova, Князева Е. Н., Салазкин М. Г., Foresight and STI Governance 2023 Vol. 17 No. 4 P. 80–91
Вызовы, с которыми сталкиваются исследования будущего, характеризуются особенной сложностью, взаимосвязанностью, противоречивостью и не поддаются разрешению линейными подходами. Прогностическая наука нуждается в инструментах, соответствующих новой контекстуальной сложности, позволяющих охватывать гораздо больший спектр движущих сил и их потенциальных эффектов в нелинейной перспективе, чтобы повысить точность прогнозов и качество стратегий. В статье посредством ретроспективного анализа прогностической науки и ...
Добавлено: 25 января 2024 г.
Рыбаков М. Н., Shkatov D., Journal of Logic and Computation 2025 Vol. 35 No. 2 Article exad078
Добавлено: 3 ноября 2023 г.
Добавлено: 7 июля 2023 г.